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Recent questions tagged summation
0
votes
1
answer
1
self doubts
What is the value of summation of n+$\frac{n}{2}$ + $\frac{n}{4}$ + …….+ 1 where n is an even positive integer ?
What is the value of summation of n+$\frac{n}{2}$ + $\frac{n}{4}$ + …….+ 1 where n is an even positive integer ?
Swarnava Bose
525
views
Swarnava Bose
asked
Jul 23, 2023
Quantitative Aptitude
arithmetic-series
general-aptitude
quantitative-aptitude
summation
+
–
5
votes
1
answer
2
Counting number of pairs whose sum is less than k
How many pairs $(x,y)$ such that $x+y <= k$, where x y and k are integers and $x,y>=0, k > 0$. Solve by summation rules. Solve by combinatorial argument.
How many pairs $(x,y)$ such that $x+y <= k$, where x y and k are integers and $x,y>=0, k 0$.Solve by summation rules.Solve by combinatorial argument.
dd
1.2k
views
dd
asked
Jun 8, 2020
Combinatory
combinatory
summation
descriptive
+
–
2
votes
2
answers
3
ISI2014-DCG-16
The sum of the series $\dfrac{1}{1.2} + \dfrac{1}{2.3}+ \cdots + \dfrac{1}{n(n+1)} + \cdots $ is $1$ $1/2$ $0$ non-existent
The sum of the series $\dfrac{1}{1.2} + \dfrac{1}{2.3}+ \cdots + \dfrac{1}{n(n+1)} + \cdots $ is$1$$1/2$$0$non-existent
Arjun
696
views
Arjun
asked
Sep 23, 2019
Quantitative Aptitude
isi2014-dcg
quantitative-aptitude
summation
+
–
1
votes
1
answer
4
ISI2014-DCG-34
The following sum of $n+1$ terms $2 + 3 \times \begin{pmatrix} n \\ 1 \end{pmatrix} + 5 \times \begin{pmatrix} n \\ 2 \end{pmatrix} + 9 \times \begin{pmatrix} n \\ 3 \end{pmatrix} + 17 \times \begin{pmatrix} n \\ 4 \end{pmatrix} + \cdots$ up to $n+1$ terms is equal to $3^{n+1}+2^{n+1}$ $3^n \times 2^n$ $3^n + 2^n$ $2 \times 3^n$
The following sum of $n+1$ terms $$2 + 3 \times \begin{pmatrix} n \\ 1 \end{pmatrix} + 5 \times \begin{pmatrix} n \\ 2 \end{pmatrix} + 9 \times \begin{pmatrix} n \\ 3 \en...
Arjun
666
views
Arjun
asked
Sep 23, 2019
Combinatory
isi2014-dcg
combinatory
binomial-theorem
summation
+
–
1
votes
0
answers
5
ISI2014-DCG-65
The sum $\dfrac{n}{n^2}+\dfrac{n}{n^2+1^2}+\dfrac{n}{n^2+2^2}+ \cdots + \dfrac{n}{n^2+(n-1)^2} + \cdots \cdots$ is $\frac{\pi}{4}$ $\frac{\pi}{8}$ $\frac{\pi}{6}$ $2 \pi$
The sum $\dfrac{n}{n^2}+\dfrac{n}{n^2+1^2}+\dfrac{n}{n^2+2^2}+ \cdots + \dfrac{n}{n^2+(n-1)^2} + \cdots \cdots$ is$\frac{\pi}{4}$$\frac{\pi}{8}$$\frac{\pi}{6}$$2 \pi$
Arjun
502
views
Arjun
asked
Sep 23, 2019
Quantitative Aptitude
isi2014-dcg
quantitative-aptitude
summation
non-gate
+
–
1
votes
1
answer
6
ISI2014-DCG-72
The sum $\sum_{k=1}^n (-1)^k \:\: {}^nC_k \sum_{j=0}^k (-1)^j \: \: {}^kC_j$ is equal to $-1$ $0$ $1$ $2^n$
The sum $\sum_{k=1}^n (-1)^k \:\: {}^nC_k \sum_{j=0}^k (-1)^j \: \: {}^kC_j$ is equal to $-1$$0$$1$$2^n$
Arjun
675
views
Arjun
asked
Sep 23, 2019
Combinatory
isi2014-dcg
combinatory
summation
+
–
2
votes
1
answer
7
ISI2015-MMA-17
Let $X=\frac{1}{1001} + \frac{1}{1002} + \frac{1}{1003} + \cdots + \frac{1}{3001}$. Then, $X \lt1$ $X\gt3/2$ $1\lt X\lt 3/2$ none of the above holds
Let $X=\frac{1}{1001} + \frac{1}{1002} + \frac{1}{1003} + \cdots + \frac{1}{3001}$. Then,$X \lt1$$X\gt3/2$$1\lt X\lt 3/2$none of the above holds
Arjun
521
views
Arjun
asked
Sep 23, 2019
Quantitative Aptitude
isi2015-mma
quantitative-aptitude
summation
+
–
0
votes
2
answers
8
ISI2015-MMA-24
The series $\sum_{k=2}^{\infty} \frac{1}{k(k-1)}$ converges to $-1$ $1$ $0$ does not converge
The series $\sum_{k=2}^{\infty} \frac{1}{k(k-1)}$ converges to$-1$$1$$0$does not converge
Arjun
605
views
Arjun
asked
Sep 23, 2019
Quantitative Aptitude
isi2015-mma
number-system
convergence-divergence
summation
non-gate
+
–
1
votes
1
answer
9
ISI2015-MMA-54
If $0 <x<1$, then the sum of the infinite series $\frac{1}{2}x^2+\frac{2}{3}x^3+\frac{3}{4}x^4+ \cdots$ is $\log \frac{1+x}{1-x}$ $\frac{x}{1-x} + \log(1+x)$ $\frac{1}{1-x} + \log(1-x)$ $\frac{x}{1-x} + \log(1-x)$
If $0 <x<1$, then the sum of the infinite series $\frac{1}{2}x^2+\frac{2}{3}x^3+\frac{3}{4}x^4+ \cdots$ is$\log \frac{1+x}{1-x}$$\frac{x}{1-x} + \log(1+x)$$\frac{1}{1-x} ...
Arjun
762
views
Arjun
asked
Sep 23, 2019
Others
isi2015-mma
summation
non-gate
+
–
0
votes
0
answers
10
ISI2015-MMA-80
Let $0 < \alpha < \beta < 1$. Then $ \Sigma_{k=1}^{\infty} \int_{1/(k+\beta)}^{1/(k+\alpha)} \frac{1}{1+x} dx$ is equal to $\log_e \frac{\beta}{\alpha}$ $\log_e \frac{1+ \beta}{1 + \alpha}$ $\log_e \frac{1+\alpha }{1+ \beta}$ $\infty$
Let $0 < \alpha < \beta < 1$. Then $$ \Sigma_{k=1}^{\infty} \int_{1/(k+\beta)}^{1/(k+\alpha)} \frac{1}{1+x} dx$$ is equal to$\log_e \frac{\beta}{\alpha}$$\log_e \frac{1+ ...
Arjun
519
views
Arjun
asked
Sep 23, 2019
Calculus
isi2015-mma
calculus
definite-integral
summation
non-gate
+
–
1
votes
2
answers
11
ISI2015-MMA-84
For positive real numbers $a_1, a_2, \cdots, a_{100}$, let $p=\sum_{i=1}^{100} a_i \text{ and } q=\sum_{1 \leq i < j \leq 100} a_ia_j.$ Then $q=\frac{p^2}{2}$ $q^2 \geq \frac{p^2}{2}$ $q< \frac{p^2}{2}$ none of the above
For positive real numbers $a_1, a_2, \cdots, a_{100}$, let $$p=\sum_{i=1}^{100} a_i \text{ and } q=\sum_{1 \leq i < j \leq 100} a_ia_j.$$ Then $q=\frac{p^2}{2}$$q^2 \geq ...
Arjun
435
views
Arjun
asked
Sep 23, 2019
Others
isi2015-mma
summation
non-gate
+
–
1
votes
4
answers
12
ISI2015-DCG-2
Let $S=\{6, 10, 7, 13, 5, 12, 8, 11, 9\}$ and $a=\underset{x \in S}{\Sigma} (x-9)^2$ & $b = \underset{x \in S}{\Sigma} (x-10)^2$. Then $a <b$ $a>b$ $a=b$ None of these
Let $S=\{6, 10, 7, 13, 5, 12, 8, 11, 9\}$ and $a=\underset{x \in S}{\Sigma} (x-9)^2$ & $b = \underset{x \in S}{\Sigma} (x-10)^2$. Then$a <b$$a>b$$a=b$None of these
gatecse
568
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
summation
+
–
0
votes
1
answer
13
ISI2015-DCG-15
The smallest integer $n$ for which $1+2+2^2+2^3+2^4+ \cdots +2^n$ exceeds $9999$, given that $\log_{10} 2=0.30103$, is $12$ $13$ $14$ None of these
The smallest integer $n$ for which $1+2+2^2+2^3+2^4+ \cdots +2^n$ exceeds $9999$, given that $\log_{10} 2=0.30103$, is$12$$13$$14$None of these
gatecse
378
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2015-dcg
quantitative-aptitude
summation
+
–
1
votes
2
answers
14
ISI2016-DCG-2
Let $S=\{6,10,7,13,5,12,8,11,9\},$ and $a=\sum_{x\in S}(x-9)^{2}\:\&\: b=\sum_{x\in S}(x-10)^{2}.$ Then $a<b$ $a>b$ $a=b$ None of these
Let $S=\{6,10,7,13,5,12,8,11,9\},$ and $a=\sum_{x\in S}(x-9)^{2}\:\&\: b=\sum_{x\in S}(x-10)^{2}.$ Then$a<b$$a>b$$a=b$None of these
gatecse
671
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2016-dcg
quantitative-aptitude
summation
inequality
+
–
0
votes
1
answer
15
ISI2016-DCG-17
The smallest integer $n$ for which $1+2+2^{2}+2^{3}+2^{4}+\cdots+2^{n}$ exceeds $9999$, given that $\log_{10}2=0.30103$, is $12$ $13$ $14$ None of these
The smallest integer $n$ for which $1+2+2^{2}+2^{3}+2^{4}+\cdots+2^{n}$ exceeds $9999$, given that $\log_{10}2=0.30103$, is$12$$13$$14$None of these
gatecse
283
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2016-dcg
quantitative-aptitude
summation
+
–
1
votes
1
answer
16
ISI2016-DCG-23
The value of $\log_{2}e-\log_{4}e+\log_{8}e-\log_{16}e+\log_{32}e-\cdots\:\:$ is $-1$ $0$ $1$ None of these
The value of $\log_{2}e-\log_{4}e+\log_{8}e-\log_{16}e+\log_{32}e-\cdots\:\:$ is$-1$$0$$1$None of these
gatecse
413
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2016-dcg
quantitative-aptitude
logarithms
summation
+
–
3
votes
2
answers
17
ISI2017-DCG-1
The value of $\dfrac{1}{\log_2 n}+ \dfrac{1}{\log_3 n}+\dfrac{1}{\log_4 n}+ \dots + \dfrac{1}{\log_{2017} n}\:\:($ where $n=2017!)$ is $1$ $2$ $2017$ none of these
The value of $\dfrac{1}{\log_2 n}+ \dfrac{1}{\log_3 n}+\dfrac{1}{\log_4 n}+ \dots + \dfrac{1}{\log_{2017} n}\:\:($ where $n=2017!)$ is$1$$2$$2017$none of these
gatecse
565
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2017-dcg
quantitative-aptitude
logarithms
summation
+
–
0
votes
1
answer
18
ISI2017-DCG-13
The value of $\dfrac{x}{1-x^2} + \dfrac{x^2}{1-x^4} + \dfrac{x^4}{1-x^8} + \dfrac{x^8}{1-x^{16}}$ is $\frac{1}{1-x^{16}}$ $\frac{1}{1-x^{12}}$ $\frac{1}{1-x} – \frac{1}{1-x^{16}}$ $\frac{1}{1-x} – \frac{1}{1-x^{12}}$
The value of $\dfrac{x}{1-x^2} + \dfrac{x^2}{1-x^4} + \dfrac{x^4}{1-x^8} + \dfrac{x^8}{1-x^{16}}$ is$\frac{1}{1-x^{16}}$$\frac{1}{1-x^{12}}$$\frac{1}{1-x} – \frac{1}{1-...
gatecse
393
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2017-dcg
quantitative-aptitude
summation
+
–
0
votes
1
answer
19
ISI2018-DCG-27
$\sum_{n=1}^{\infty}\frac{1}{n(n+1)}$ is $2$ $1$ $\infty$ not a convergent series
$\sum_{n=1}^{\infty}\frac{1}{n(n+1)}$ is$2$$1$$\infty$not a convergent series
gatecse
390
views
gatecse
asked
Sep 18, 2019
Quantitative Aptitude
isi2018-dcg
quantitative-aptitude
sequence-series
summation
+
–
2
votes
1
answer
20
Kenneth Rosen Edition 6th Exercise 2.4 Question 15c (Page No. 161)
$\sum_{j=2}^{8}(-3)^j$
$\sum_{j=2}^{8}(-3)^j$
aditi19
445
views
aditi19
asked
Dec 5, 2018
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
sequence-series
summation
+
–
3
votes
1
answer
21
ISI2016-MMA-18
Let $A=\begin{pmatrix} -1 & 2 \\ 0 & -1 \end{pmatrix}$, and $B=A+A^2+A^3+ \dots +A^{50}$. Then $B^2 =1$ $B^2 =0$ $B^2 =A$ $B^2 =B$
Let $A=\begin{pmatrix} -1 & 2 \\ 0 & -1 \end{pmatrix}$, and $B=A+A^2+A^3+ \dots +A^{50}$. Then$B^2 =1$$B^2 =0$$B^2 =A$$B^2 =B$
go_editor
299
views
go_editor
asked
Sep 13, 2018
Linear Algebra
isi2016-mmamma
linear-algebra
matrix
summation
+
–
0
votes
0
answers
22
ISI2016-MMA-22
The infinite series $\Sigma_{n=1}^{\infty} \frac{a^n \log n}{n^2}$ converges if and only if $a \in [-1, 1)$ $a \in (-1, 1]$ $a \in [-1, 1]$ $a \in (-\infty, \infty)$
The infinite series $\Sigma_{n=1}^{\infty} \frac{a^n \log n}{n^2}$ converges if and only if$a \in [-1, 1)$$a \in (-1, 1]$$a \in [-1, 1]$$a \in (-\infty, \infty)$
go_editor
250
views
go_editor
asked
Sep 13, 2018
Others
isi2016-mmamma
sequence-series
convergence-divergence
summation
non-gate
+
–
2
votes
1
answer
23
Infinite series
Find the infinite sum of the series $1 + \frac{4}{7} + \frac{9}{7^2} + \frac{16}{7^3} + \frac{25}{7^4} + .............\Join$
Find the infinite sum of the series$1 + \frac{4}{7} + \frac{9}{7^2} + \frac{16}{7^3} + \frac{25}{7^4} + .............\Join$
pankaj_vir
1.3k
views
pankaj_vir
asked
Aug 8, 2018
Quantitative Aptitude
quantitative-aptitude
summation
+
–
0
votes
0
answers
24
Bounding Summation
How does the below bounds to logn? Please explain the steps 1 and 2. I came to know that they are using the idea of splitting the summations and bounding them. How the first and second step came?
How does the below bounds to logn?Please explain the steps 1 and 2.I came to know that they are using the idea of splitting the summations and bounding them.How the first...
Ayush Upadhyaya
1.1k
views
Ayush Upadhyaya
asked
May 11, 2018
Algorithms
summation
+
–
1
votes
1
answer
25
addition
value of 1/3 + 1/15 + 1/35 +............................+1/9999 a)100/101 b)50/101 c)100/51 d)50/51
value of 1/3 + 1/15 + 1/35 +............................+1/9999a)100/101b)50/101c)100/51d)50/51
A_i_$_h
1.5k
views
A_i_$_h
asked
Sep 12, 2017
Quantitative Aptitude
quantitative-aptitude
summation
number-series
+
–
5
votes
1
answer
26
Series Summation
Series summation of $S_n$ in closed form? $\begin{align*} &S_n = \frac{1}{1.2.3.4} + \frac{1}{2.3.4.5} + \frac{1}{3.4.5.6} + \dots + \frac{1}{n.(n+1).(n+2).(n+3)} \end{align*}$
Series summation of $S_n$ in closed form?$\begin{align*} &S_n = \frac{1}{1.2.3.4} + \frac{1}{2.3.4.5} + \frac{1}{3.4.5.6} + \dots + \frac{1}{n.(n+1).(n+2).(n+3)} \end{ali...
dd
811
views
dd
asked
Jun 11, 2017
Set Theory & Algebra
number-theory
summation
discrete-mathematics
+
–
3
votes
2
answers
27
Manipulation of sum
Prove the identity: $\begin{align*} &\sum_{i=0}^{n}\sum_{j=0}^{i} a_ia_j = \frac{1}{2}\left ( \left ( \sum_{i=0}^{n}a_i \right )^2 + \left ( \sum_{i=0}^{n}a_i^2 \right )\right ) \end{align*}$
Prove the identity:$$\begin{align*} &\sum_{i=0}^{n}\sum_{j=0}^{i} a_ia_j = \frac{1}{2}\left ( \left ( \sum_{i=0}^{n}a_i \right )^2 + \left ( \sum_{i=0}^{n}a_i^2 \right )\...
dd
826
views
dd
asked
Feb 25, 2017
Combinatory
discrete-mathematics
summation
+
–
2
votes
0
answers
28
summation series
what is the summation of this series? S=nC0*20+nC1*21+nC2*22+..............nCn*2n
what is the summation of this series?S=nC0*20+nC1*21+nC2*22+..............nCn*2n
firki lama
440
views
firki lama
asked
Jan 17, 2017
Combinatory
summation
+
–
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