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Recent questions tagged kenneth-rosen
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511
Kenneth Rosen Edition 7 Exercise 2.4 Question 26 (Page No. 169)
For each of these lists of integers, provide a simple formula or rule that generates the terms of an integer sequence that begins with the given list.Assuming that your formula or rule is correct, determine the next three terms of the sequence. ... $2, 4, 16, 256, 65536, 4294967296,\dots$
For each of these lists of integers, provide a simple formula or rule that generates the terms of an integer sequence that begins with the given list.Assuming that your f...
admin
166
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admin
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Apr 20, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
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0
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512
Kenneth Rosen Edition 7 Exercise 2.4 Question 25 (Page No. 169)
For each of these lists of integers, provide a simple formula or rule that generates the terms of an integer sequence that begins with the given list.Assuming that your formula or rule is correct, determine the next three terms of the sequence. ... $2, 3, 7, 25, 121, 721, 5041, 40321,\dots$
For each of these lists of integers, provide a simple formula or rule that generates the terms of an integer sequence that begins with the given list.Assuming that your f...
admin
258
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admin
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Apr 20, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
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0
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0
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513
Kenneth Rosen Edition 7 Exercise 2.4 Question 24 (Page No. 169)
Find a recurrence relation for the balance $B(k)$ owed at the end of $k$ months on a loan at a rate of $r$ if a payment $P$ is made on the loan each month. $[$Hint: Express $B(k)$ in terms of $B(k − 1)$ ... monthly interest rate is $r/12.]$ Determine what the monthly payment $P$ should be so that the loan is paid off after $T$ months.
Find a recurrence relation for the balance $B(k)$ owed at the end of $k$ months on a loan at a rate of $r$ if a payment $P$ is made on the loan each month. $[$Hint: Expre...
admin
313
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admin
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Apr 20, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
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0
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0
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514
Kenneth Rosen Edition 7 Exercise 2.4 Question 23 (Page No. 169)
Find a recurrence relation for the balance $B(k)$ owed at the end of $k$ months on a loan of $\$5000$ at a rate of $7\%$ if a payment of $\$100$ is made each month. $[$Hint: Express $B(k)$ in terms of $B(k − 1);$ the monthly interest is $(0.07/12)B(k − 1).]$
Find a recurrence relation for the balance $B(k)$ owed at the end of $k$ months on a loan of $\$5000$ at a rate of $7\%$ if a payment of $\$100$ is made each month. $[$Hi...
admin
292
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admin
asked
Apr 20, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
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0
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0
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515
Kenneth Rosen Edition 7 Exercise 2.4 Question 22 (Page No. 168 - 169)
An employee joined a company in $2009$ with a starting salary of $\$50,000.$ Every year this employee receives a raise of $\$1000$ plus $5\%$ of the salary of the previous year. Set up a recurrence relation for the ... of this employee be in $2017?$ Find an explicit formula for the salary of this employee $n$ years after $2009.$
An employee joined a company in $2009$ with a starting salary of $\$50,000.$ Every year this employee receives a raise of $\$1000$ plus $5\%$ of the salary of the previou...
admin
184
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admin
asked
Apr 20, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
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0
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516
Kenneth Rosen Edition 7 Exercise 2.4 Question 21 (Page No. 168)
A factory makes custom sports cars at an increasing rate. In the first month, only one car is made, in the second month, two cars are made, and so on, with $n$ cars made in the $nth$ month. Set up a recurrence ... in the first year? Find an explicit formula for the number of cars produced in the first $n$ months by this factory
A factory makes custom sports cars at an increasing rate. In the first month, only one car is made, in the second month, two cars are made, and so on, with $n$ cars made ...
admin
338
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admin
asked
Apr 20, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
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–
0
votes
0
answers
517
Kenneth Rosen Edition 7 Exercise 2.4 Question 20 (Page No. 168)
Assume that the population of the world in $2010$ was $6.9$ billion and is growing at the rate of $1.1\%$ a year. Set up a recurrence relation for the population of the world $n$ years after $2010.$ Find an explicit formula for the population of the world $n$ years after $2010.$ What will the population of the world be in $2030?$
Assume that the population of the world in $2010$ was $6.9$ billion and is growing at the rate of $1.1\%$ a year.Set up a recurrence relation for the population of the wo...
admin
199
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admin
asked
Apr 20, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
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–
0
votes
0
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518
Kenneth Rosen Edition 7 Exercise 2.4 Question 19 (Page No. 168)
Suppose that the number of bacteria in a colony triples every hour. Set up a recurrence relation for the number of bacteria after n hours have elapsed. If $100$ bacteria are used to begin a new colony, how many bacteria will be in the colony in $10$ hours?
Suppose that the number of bacteria in a colony triples every hour.Set up a recurrence relation for the number of bacteria after n hours have elapsed.If $100$ bacteria ar...
admin
184
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admin
asked
Apr 20, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
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0
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0
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519
Kenneth Rosen Edition 7 Exercise 2.4 Question 18 (Page No. 168)
A person deposits $\$1000$ in an account that yields $9\%$ interest compounded annually. Set up a recurrence relation for the amount in the account at the end of $n$ years. Find an explicit formula for the amount in the account at the end of $n$ years. How much money will the account contain after $100$ years?
A person deposits $\$1000$ in an account that yields $9\%$ interest compounded annually.Set up a recurrence relation for the amount in the account at the end of $n$ years...
admin
204
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admin
asked
Apr 20, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
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0
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0
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520
Kenneth Rosen Edition 7 Exercise 2.4 Question 17 (Page No. 168)
Find the solution to each of these recurrence relations and initial conditions. Use an iterative approach such as that used in Example $10.$ $a_{n} = 3a_{n−1}, a_{0} = 2$ $a_{n} = a_{n−1} + 2, a_{0} = 3$ $a_{n} = a_{n−1} + n, a_{0} = 1$ ... $a_{n} = na_{n−1}, a_{0} = 5$ $a_{n} = 2na_{n−1}, a_{0} = 1$
Find the solution to each of these recurrence relations and initial conditions. Use an iterative approach such as that used in Example $10.$$a_{n} = 3a_{n−1}, a_{0} = 2...
admin
175
views
admin
asked
Apr 20, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
+
–
0
votes
0
answers
521
Kenneth Rosen Edition 7 Exercise 2.4 Question 16 (Page No. 168)
Find the solution to each of these recurrence relations with the given initial conditions. Use an iterative approach such as that used in Example $10.$ $a_{n} = −a_{n−1}, a_{0} = 5$ $a_{n} = a_{n−1} + 3, a_{0} = 1$ $a_{n} = a_{n−1} − n, a_{0} = 4$ ... $a_{n} = 2na_{n−1}, a_{0} = 3$ $a_{n} = −a_{n−1} + n − 1, a_{0} = 7$
Find the solution to each of these recurrence relations with the given initial conditions. Use an iterative approach such as that used in Example $10.$$a_{n} = −a_{n−...
admin
181
views
admin
asked
Apr 20, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
+
–
0
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0
answers
522
Kenneth Rosen Edition 7 Exercise 2.4 Question 15 (Page No. 168)
Show that the sequence $\{a_{n}\}$ is a solution of the recurrence relation $a_{n} = a_{n−1} + 2a_{n−2} + 2n − 9$ if $a_{n} = −n + 2.$ $a_{n} = 5(−1)^{n} − n + 2.$ $a_{n} = 3(−1)^{n} + 2^{n} − n + 2.$ $a_{n} = 7 \cdot 2^{n} − n + 2.$
Show that the sequence $\{a_{n}\}$ is a solution of the recurrence relation $a_{n} = a_{n−1} + 2a_{n−2} + 2n − 9$ if$a_{n} = −n + 2.$$a_{n} = 5(−1)^{n} − n + ...
admin
201
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admin
asked
Apr 19, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
+
–
0
votes
0
answers
523
Kenneth Rosen Edition 7 Exercise 2.4 Question 14 (Page No. 168)
For each of these sequences find a recurrence relation satisfied by this sequence. (The answers are not unique because there are infinitely many different recurrence relations satisfied by any sequence.) $a_{n} = 3$ $a_{n} = 2n$ $a_{n} = 2n + 3$ $a_{n} = 5^{n}$ $a_{n} = n^{2}$ $a_{n} = n^{2} + n$ $a_{n} = n + (−1)^{n}$ $a_{n} = n!$
For each of these sequences find a recurrence relation satisfied by this sequence. (The answers are not unique because there are infinitely many different recurrence rela...
admin
339
views
admin
asked
Apr 19, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
+
–
0
votes
0
answers
524
Kenneth Rosen Edition 7 Exercise 2.4 Question 13 (Page No. 168)
Is the sequence $\{a_{n}\}$ a solution of the recurrence relation $a_{n} = 8a_{n−1} − 16a_{n−2}$ if $a_{n} = 0$ $a{n} = 1$ $a_{n} = 2^{n}$ $a_{n} = 4^{n}$ $a_{n} = n4^{n}$ $a_{n} = 2 \cdot 4^{n} + 3n4^{n}$ $a_{n} = (−4)^{n}$ $a_{n} = n^{2}4^{n}$
Is the sequence $\{a_{n}\}$ a solution of the recurrence relation $a_{n} = 8a_{n−1} − 16a_{n−2}$ if$a_{n} = 0$$a{n} = 1$$a_{n} = 2^{n}$$a_{n} = 4^{n}$$a_{n} = n4^{n...
admin
161
views
admin
asked
Apr 19, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
+
–
0
votes
0
answers
525
Kenneth Rosen Edition 7 Exercise 2.4 Question 12 (Page No. 168)
Show that the sequence $\{a_{n}\}$ is a solution of the recurrence relation $a_{n} = −3a_{n−1} + 4a_{n−2}$ if $a_{n} = 0.$ $an = 1.$ $a_{n} = (−4)^{n}.$ $a_{n} = 2(−4)^{n} + 3.$
Show that the sequence $\{a_{n}\}$ is a solution of the recurrence relation $a_{n} = −3a_{n−1} + 4a_{n−2}$ if$a_{n} = 0.$$an = 1.$$a_{n} = (−4)^{n}.$ $a_{n} = 2(�...
admin
192
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admin
asked
Apr 19, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
+
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0
votes
0
answers
526
Kenneth Rosen Edition 7 Exercise 2.4 Question 11 (Page No. 168)
Let $a_{n} = 2^{n} + 5 \cdot 3^{n}$ for $n = 0, 1, 2,\dots$ Find $a_{0} a_{1}, a_{2}, a_{3},$ and $a_{4}.$ Show that $a_{2} = 5a_{1} − 6a_{0}, a_{3} = 5a_{2} − 6a_{1},$ and $a_{4} = 5a_{3} − 6a_{2}.$ Show that $an = 5a_{n−1} − 6a_{n−2}$ for all integers $n$ with $n \geq 2.$
Let $a_{n} = 2^{n} + 5 \cdot 3^{n}$ for $n = 0, 1, 2,\dots$Find $a_{0} a_{1}, a_{2}, a_{3},$ and $a_{4}.$Show that $a_{2} = 5a_{1} − 6a_{0}, a_{3} = 5a_{2} − 6a_{1},$...
admin
211
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admin
asked
Apr 19, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
+
–
0
votes
0
answers
527
Kenneth Rosen Edition 7 Exercise 2.4 Question 10 (Page No. 168)
Find the first six terms of the sequence defined by each of these recurrence relations and initial conditions. $a_{n} = −2a_{n−1}, a_{0} = −1$ $a_{n} = a_{n−1} − a_{n−2}, a_{0} = 2, a_{1} = −1$ $a_{n} = 3a^{2}_{n−1}, a_{0} = 1$ ... $a_{n} = a_{n−1} − a_{n−2} + a_{n−3}, a_{0} = 1, a_{1} = 1, a_{2} = 2$
Find the first six terms of the sequence defined by each of these recurrence relations and initial conditions.$a_{n} = −2a_{n−1}, a_{0} = −1$$a_{n} = a_{n−1} − ...
admin
253
views
admin
asked
Apr 19, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
+
–
0
votes
1
answer
528
Kenneth Rosen Edition 7 Exercise 2.4 Question 9 (Page No. 168)
Find the first five terms of the sequence defined by each of these recurrence relations and initial conditions. $a_{n} = 6a_{n−1}, a_{0} = 2$ $a_{n} = a_{n−1}^{2}, a_{1} = 2$ $a_{n} = a_{n−1} + 3a_{n−2}, a_{0} = 1, a_{1} = 2$ ... $a_{n} = a_{n−1} + a_{n−3}, a_{0} = 1, a_{1} = 2, a_{2} = 0$
Find the first five terms of the sequence defined by each of these recurrence relations and initial conditions.$a_{n} = 6a_{n−1}, a_{0} = 2$$a_{n} = a_{n−1}^{2}, a_{1...
admin
378
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admin
asked
Apr 19, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
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–
0
votes
1
answer
529
Kenneth Rosen Edition 7 Exercise 2.4 Question 8 (Page No. 168)
Find at least three different sequences beginning with the terms $3, 5, 7$ whose terms are generated by a simple formula or rule.
Find at least three different sequences beginning with the terms $3, 5, 7$ whose terms are generated by a simple formula or rule.
admin
1.9k
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admin
asked
Apr 19, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
+
–
0
votes
1
answer
530
Kenneth Rosen Edition 7 Exercise 2.4 Question 7 (Page No. 168)
Find at least three different sequences beginning with the terms $1, 2, 4$ whose terms are generated by a simple formula or rule.
Find at least three different sequences beginning with the terms $1, 2, 4$ whose terms are generated by a simple formula or rule.
admin
500
views
admin
asked
Apr 19, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
+
–
1
votes
1
answer
531
Kenneth Rosen Edition 7 Exercise 2.4 Question 6 (Page No. 167 - 168)
List the first $10$ terms of each of these sequences. the sequence obtained by starting with $10$ and obtaining each term by subtracting $3$ from the previous term the sequence whose nth term is the sum of the first $n$ positive ... $2,$ and so on the sequence whose nth term is the largest integer $k$ such that $k! \leq n$
List the first $10$ terms of each of these sequences.the sequence obtained by starting with $10$ and obtaining each term by subtracting $3$ from the previous termthe sequ...
admin
3.3k
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admin
asked
Apr 19, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
+
–
0
votes
1
answer
532
Kenneth Rosen Edition 7 Exercise 2.4 Question 5 (Page No. 167)
List the first $10$ terms of each of these sequences. the sequence that begins with $2$ and in which each successive term is $3$ more than the preceding term the sequence that lists each positive integer three times, in increasing ... $nth$ term is the number of letters in the English word for the index $n$
List the first $10$ terms of each of these sequences.the sequence that begins with $2$ and in which each successive term is $3$ more than the preceding termthe sequence t...
admin
1.7k
views
admin
asked
Apr 19, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
+
–
0
votes
1
answer
533
Kenneth Rosen Edition 7 Exercise 2.4 Question 4 (Page No. 167)
What are the terms $a_{0}, a_{1}, a_{2},$ and $a_{3}$ of the sequence $\{a_{n}\},$ where $a_{n}$ equals $(-2)^{n}$ $3$ $7+4^{n}$ $2^{n} + (-2)^{n}$
What are the terms $a_{0}, a_{1}, a_{2},$ and $a_{3}$ of the sequence $\{a_{n}\},$ where $a_{n}$ equals$(-2)^{n}$$3$$7+4^{n}$$2^{n} + (-2)^{n}$
admin
312
views
admin
asked
Apr 19, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
+
–
0
votes
1
answer
534
Kenneth Rosen Edition 7 Exercise 2.4 Question 3 (Page No. 167)
What are the terms $a_{0}, a_{1}, a_{2},$ and $a_{3}$ of the sequence $\{a_{n}\},$ where $a_{n}$ equals $2^{n} + 1$ $(n + 1)^{n+1}$ $\left \lfloor n/2\right \rfloor$ $\left \lfloor n/2\right \rfloor + \left \lceil n/2\right \rceil$
What are the terms $a_{0}, a_{1}, a_{2},$ and $a_{3}$ of the sequence $\{a_{n}\},$ where $a_{n}$ equals$2^{n} + 1$$(n + 1)^{n+1}$$\left \lfloor n/2\right \rfloor$$\left \...
admin
206
views
admin
asked
Apr 19, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
+
–
0
votes
1
answer
535
Kenneth Rosen Edition 7 Exercise 2.4 Question 2 (Page No. 167)
What is the term $a_{8}$ of the sequence $\{a_{n}\},$ if $a_{n}$ equals $2^{n−1}$ $7$ $1 + (−1)^{n}$ $−(−2)^{n}$
What is the term $a_{8}$ of the sequence $\{a_{n}\},$ if $a_{n}$ equals$2^{n−1}$$7$$1 + (−1)^{n}$$−(−2)^{n}$
admin
242
views
admin
asked
Apr 19, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
+
–
0
votes
1
answer
536
Kenneth Rosen Edition 7 Exercise 2.4 Question 1 (Page No. 167)
Find these terms of the sequence $\{a_{n}\},$ where $a_{n} = 2\cdot(−3)^{n} + 5^{n}.$ $a_{0}$ $a_{1}$ $a_{4}$ $a_{5}$
Find these terms of the sequence $\{a_{n}\},$ where $a_{n} = 2\cdot(−3)^{n} + 5^{n}.$$a_{0}$$a_{1}$$a_{4}$$a_{5}$
admin
269
views
admin
asked
Apr 19, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
+
–
1
votes
2
answers
537
Rosen 7e Exercise-8.5 Question-15 page no-558 Inclusion-Exclusion
How many permutations of the 10 digits either begin with the 3 digits 987, contain the digits 45 in the fifth and sixth positions, or end with the 3 digits 123?
How many permutations of the 10 digits either begin with the 3 digits 987, contain the digits 45 in the fifth and sixth positions, or end with the 3 digits 123?
aditi19
1.2k
views
aditi19
asked
May 24, 2019
Combinatory
discrete-mathematics
kenneth-rosen
inclusion-exclusion
+
–
0
votes
0
answers
538
Discrete Mathematics by Kenneth Rosen,section2.4,recursive functions
$C_{a}^{k}:\mathbb{N}^{k}\rightarrow \mathbb{N}$ I am studying discrete math from beginnings and came across this term in primitive recursive function.I don't know what $C_{a}^{k}$ means and does $\mathbb{N}$ means set of natural numbers?Someone please help me out.
$C_{a}^{k}:\mathbb{N}^{k}\rightarrow \mathbb{N}$I am studying discrete math from beginnings and came across this term in primitive recursive function.I don't know what $C...
souren
396
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souren
asked
May 15, 2019
Set Theory & Algebra
discrete-mathematics
set-theory&algebra
kenneth-rosen
+
–
0
votes
0
answers
539
Rosen 7e Exercise 8.2 Questionno-26 page no-525 Recurrence Relation
What is the general form of the particular solution guaranteed to exist of the linear nonhomogeneous recurrence relation $a_n$=$6a_{n-1}$-$12a_{n-2}$+$8a_{n-3}$+F(n) if F(n)=$n^2$ F(n)=$2^n$ F(n)=$n2^n$ F(n)=$(-2)^n$ F(n)=$n^22^n$ F(n)=$n^3(-2)^n$ F(n)=3
What is the general form of the particular solution guaranteed to exist of the linear nonhomogeneous recurrence relation$a_n$=$6a_{n-1}$-$12a_{n-2}$+$8a_{n-3}$+F(n) ifF(n...
aditi19
543
views
aditi19
asked
May 14, 2019
Combinatory
kenneth-rosen
discrete-mathematics
recurrence-relation
+
–
0
votes
0
answers
540
Rosen 7e Exercise-8.2 Question no-23 page no-525 Recurrence Relation
Consider the nonhomogeneous linear recurrence relation $a_n$=$3a_{n-1}$+$2^n$ in the book solution is given $a_n$=$-2^{n+1}$ but I’m getting $a_n$=$3^{n+1}-2^{n+1}$
Consider the nonhomogeneous linear recurrence relation $a_n$=$3a_{n-1}$+$2^n$in the book solution is given $a_n$=$-2^{n+1}$but I’m getting $a_n$=$3^{n+1}-2^{n+1}$
aditi19
630
views
aditi19
asked
May 13, 2019
Combinatory
kenneth-rosen
discrete-mathematics
recurrence-relation
+
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