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Kenneth Rosen Edition 7 Exercise 8.2 Question 42 (Page No. 526)
Show that if $a_{n} = a_{n-1} + a_{n-2}, a_{0} = s\:\text{and}\: a_{1} = t,$ where $s$ and $t$ are constants, then $a_{n} = sf_{n-1} + tf_{n}$ for all positive integers $n.$
Show that if $a_{n} = a_{n-1} + a_{n-2}, a_{0} = s\:\text{and}\: a_{1} = t,$ where $s$ and $t$ are constants, then $a_{n} = sf_{n-1} + tf_{n}$ for all positive integers $...
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Kenneth Rosen Edition 7 Exercise 8.2 Question 40 (Page No. 526)
Solve the simultaneous recurrence relations $a_{n} = 3a_{n-1} + 2b_{n-1}$ $b_{n} = a_{n-1} + 2b_{n-1}$ with $a_{0} = 1 \: \text{and}\: b_{0} = 2.$
Solve the simultaneous recurrence relations$a_{n} = 3a_{n-1} + 2b_{n-1}$$b_{n} = a_{n-1} + 2b_{n-1}$with $a_{0} = 1 \: \text{and}\: b_{0} = 2.$
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Kenneth Rosen Edition 7 Exercise 8.2 Question 35 (Page No. 526)
Find the solution of the recurrence relation $a_{n} = 4a_{n-1} - 3a_{n-2} + 2^{n} + n + 3\:\text{with}\: a_{0} = 1\:\text{and}\: a_{1} = 4.$
Find the solution of the recurrence relation $a_{n} = 4a_{n-1} - 3a_{n-2} + 2^{n} + n + 3\:\text{with}\: a_{0} = 1\:\text{and}\: a_{1} = 4.$
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Kenneth Rosen Edition 7 Exercise 8.2 Question 34 (Page No. 526)
Find all solutions of the recurrence relation $a_{n} =7a_{n-1} - 16a_{n-2} + 12a_{n-3} + n4^{n}\:\text{with}\: a_{0} = -2,a_{1} = 0,\:\text{and}\: a_{2} = 5.$
Find all solutions of the recurrence relation $a_{n} =7a_{n-1} - 16a_{n-2} + 12a_{n-3} + n4^{n}\:\text{with}\: a_{0} = -2,a_{1} = 0,\:\text{and}\: a_{2} = 5.$
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Kenneth Rosen Edition 7 Exercise 8.2 Question 30 (Page No. 525)
Find all solutions of the recurrence relation $a_{n} = -5a_{n-1} - 6a_{n-2} + 42 \cdot 4^{n}.$ Find the solution of this recurrence relation with $a_{1} = 56\:\text{and}\: a_{2} = 278.$
Find all solutions of the recurrence relation $a_{n} = -5a_{n-1} - 6a_{n-2} + 42 \cdot 4^{n}.$Find the solution of this recurrence relation with $a_{1} = 56\:\text{and}\:...
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Kenneth Rosen Edition 7 Exercise 8.2 Question 29 (Page No. 525)
Find all solutions of the recurrence relation $a_{n} = 2a_{n-1} + 3n.$ Find the solution of the recurrence relation in part $(A)$ with initial condition $a_{1} = 5.$
Find all solutions of the recurrence relation $a_{n} = 2a_{n-1} + 3n.$Find the solution of the recurrence relation in part $(A)$ with initial condition $a_{1} = 5.$
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Kenneth Rosen Edition 7 Exercise 8.2 Question 28 (Page No. 525)
Find all solutions of the recurrence relation $a_{n} = 2a_{n-1} + 2n^{2}.$ Find the solution of the recurrence relation in part $(A)$ with initial condition $a_{1} = 4.$
Find all solutions of the recurrence relation $a_{n} = 2a_{n-1} + 2n^{2}.$Find the solution of the recurrence relation in part $(A)$ with initial condition $a_{1} = 4.$
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Kenneth Rosen Edition 7 Exercise 8.2 Question 22 (Page No. 525)
What is the general form of the solutions of a linear homogeneous recurrence relation if its characteristic equation has the roots $-1, -1, -1, 2, 2, 5, 5, 7?$
What is the general form of the solutions of a linear homogeneous recurrence relation if its characteristic equation has the roots $-1, -1, -1, 2, 2, 5, 5, 7?$
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86
Kenneth Rosen Edition 7 Exercise 8.2 Question 21 (Page No. 525)
What is the general form of the solutions of a linear homogeneous recurrence relation if its characteristic equation has roots $1,1,1,1,−2,−2,−2,3,3,−4?$
What is the general form of the solutions of a linear homogeneous recurrence relation if its characteristic equation has roots $1,1,1,1,−2,−2,−2,3,3,−4?$
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Kenneth Rosen Edition 7 Exercise 8.2 Question 19 (Page No. 525)
Solve the recurrence relation $a_{n} = −3a_{n−1} − 3a_{n−2} − a_{n−3}\:\text{with}\: a_{0} = 5, a_{1} = −9,\:\text{and}\: a_{2} = 15.$
Solve the recurrence relation $a_{n} = −3a_{n−1} − 3a_{n−2} − a_{n−3}\:\text{with}\: a_{0} = 5, a_{1} = −9,\:\text{and}\: a_{2} = 15.$
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Kenneth Rosen Edition 7 Exercise 8.2 Question 18 (Page No. 525)
Solve the recurrence relation $a_{n} = 6a_{n−1} − 12a_{n−2} + 8a_{n−3} \:\text{with}\: a_{0} = −5, a_{1} = 4,\: \text{and}\: a_{2} = 88.$
Solve the recurrence relation $a_{n} = 6a_{n−1} − 12a_{n−2} + 8a_{n−3} \:\text{with}\: a_{0} = −5, a_{1} = 4,\: \text{and}\: a_{2} = 88.$
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