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Recent questions tagged summation
4
votes
1
answer
1
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.
dd
asked
in
Combinatory
Jun 8, 2020
by
dd
883
views
combinatory
summation
descriptive
2
votes
2
answers
2
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
Arjun
asked
in
Quantitative Aptitude
Sep 23, 2019
by
Arjun
410
views
isi2014-dcg
quantitative-aptitude
summation
1
vote
1
answer
3
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 $3^{n+1}+2^{n+1}$ $3^n \times 2^n$ $3^n + 2^n$ $2 \times 3^n$
Arjun
asked
in
Combinatory
Sep 23, 2019
by
Arjun
363
views
isi2014-dcg
combinatory
binomial-theorem
summation
1
vote
0
answers
4
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 $\frac{\pi}{4}$ $\frac{\pi}{8}$ $\frac{\pi}{6}$ $2 \pi$
Arjun
asked
in
Quantitative Aptitude
Sep 23, 2019
by
Arjun
327
views
isi2014-dcg
quantitative-aptitude
summation
non-gate
1
vote
1
answer
5
ISI2014-DCG-72
The sum $\sum_{k=1}^n (-1)^k \:\: {}^nC_k \sum_{j=0}^k (-1)^j \: \: {}^kC_j$ is equal to $-1$ $0$ $1$ $2^n$
Arjun
asked
in
Combinatory
Sep 23, 2019
by
Arjun
367
views
isi2014-dcg
combinatory
summation
2
votes
1
answer
6
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
Arjun
asked
in
Quantitative Aptitude
Sep 23, 2019
by
Arjun
396
views
isi2015-mma
quantitative-aptitude
summation
0
votes
2
answers
7
ISI2015-MMA-24
The series $\sum_{k=2}^{\infty} \frac{1}{k(k-1)}$ converges to $-1$ $1$ $0$ does not converge
Arjun
asked
in
Quantitative Aptitude
Sep 23, 2019
by
Arjun
373
views
isi2015-mma
number-system
convergence-divergence
summation
non-gate
1
vote
1
answer
8
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 $\log \frac{1+x}{1-x}$ $\frac{x}{1-x} + \log(1+x)$ $\frac{1}{1-x} + \log(1-x)$ $\frac{x}{1-x} + \log(1-x)$
Arjun
asked
in
Others
Sep 23, 2019
by
Arjun
469
views
isi2015-mma
summation
non-gate
0
votes
0
answers
9
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 $\log_e \frac{\beta}{\alpha}$ $\log_e \frac{1+ \beta}{1 + \alpha}$ $\log_e \frac{1+\alpha }{1+ \beta}$ $\infty$
Arjun
asked
in
Calculus
Sep 23, 2019
by
Arjun
309
views
isi2015-mma
calculus
definite-integral
summation
non-gate
1
vote
1
answer
10
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
Arjun
asked
in
Others
Sep 23, 2019
by
Arjun
258
views
isi2015-mma
summation
non-gate
1
vote
4
answers
11
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
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
338
views
isi2015-dcg
quantitative-aptitude
summation
0
votes
1
answer
12
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
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
183
views
isi2015-dcg
quantitative-aptitude
summation
1
vote
2
answers
13
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
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
327
views
isi2016-dcg
quantitative-aptitude
summation
inequality
0
votes
1
answer
14
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
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
175
views
isi2016-dcg
quantitative-aptitude
summation
0
votes
1
answer
15
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
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
218
views
isi2016-dcg
quantitative-aptitude
logarithms
summation
1
vote
2
answers
16
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
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
339
views
isi2017-dcg
quantitative-aptitude
logarithms
summation
0
votes
1
answer
17
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 $\frac{1}{1-x^{16}}$ $\frac{1}{1-x^{12}}$ $\frac{1}{1-x} – \frac{1}{1-x^{16}}$ $\frac{1}{1-x} – \frac{1}{1-x^{12}}$
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
232
views
isi2017-dcg
quantitative-aptitude
summation
0
votes
1
answer
18
ISI2018-DCG-27
$\sum_{n=1}^{\infty}\frac{1}{n(n+1)}$ is $2$ $1$ $\infty$ not a convergent series
gatecse
asked
in
Quantitative Aptitude
Sep 18, 2019
by
gatecse
213
views
isi2018-dcg
quantitative-aptitude
sequence-series
summation
2
votes
1
answer
19
Kenneth Rosen Edition 6th Exercise 2.4 Question 15c (Page No. 161)
$\sum_{j=2}^{8}(-3)^j$
aditi19
asked
in
Set Theory & Algebra
Dec 5, 2018
by
aditi19
287
views
kenneth-rosen
discrete-mathematics
set-theory&algebra
sequence-series
summation
3
votes
1
answer
20
ISI2016-MMA-18
Let $A=\begin{pmatrix} -1 & 2 \\ 0 & -1 \end{pmatrix}$, and $B=A+A^2+A^3+ \dots +A^{50}$. Then $B^2 =1$ $B^2 =0$ $B^2 =A$ $B^2 =B$
go_editor
asked
in
Linear Algebra
Sep 13, 2018
by
go_editor
199
views
isi2016-mmamma
linear-algebra
matrix
summation
0
votes
0
answers
21
ISI2016-MMA-22
The infinite series $\Sigma_{n=1}^{\infty} \frac{a^n \log n}{n^2}$ converges if and only if $a \in [-1, 1)$ $a \in (-1, 1]$ $a \in [-1, 1]$ $a \in (-\infty, \infty)$
go_editor
asked
in
Others
Sep 13, 2018
by
go_editor
186
views
isi2016-mmamma
sequence-series
convergence-divergence
summation
non-gate
2
votes
1
answer
22
Infinite series
Find the infinite sum of the series $1 + \frac{4}{7} + \frac{9}{7^2} + \frac{16}{7^3} + \frac{25}{7^4} + .............\Join$
pankaj_vir
asked
in
Quantitative Aptitude
Aug 8, 2018
by
pankaj_vir
764
views
quantitative-aptitude
summation
0
votes
0
answers
23
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?
Ayush Upadhyaya
asked
in
Algorithms
May 11, 2018
by
Ayush Upadhyaya
731
views
summation
1
vote
1
answer
24
addition
value of 1/3 + 1/15 + 1/35 +............................+1/9999 a)100/101 b)50/101 c)100/51 d)50/51
A_i_$_h
asked
in
Quantitative Aptitude
Sep 12, 2017
by
A_i_$_h
1.2k
views
quantitative-aptitude
summation
number-series
5
votes
1
answer
25
Series Summation
Series summation of $S_n$ in closed form? $\begin{align*} &S_n = \frac{1}{1.2.3.4} + \frac{1}{2.3.4.5} + \frac{1}{3.4.5.6} + \dots + \frac{1}{n.(n+1).(n+2).(n+3)} \end{align*}$
dd
asked
in
Set Theory & Algebra
Jun 11, 2017
by
dd
555
views
number-theory
summation
discrete-mathematics
3
votes
2
answers
26
Manipulation of sum
Prove the identity: $\begin{align*} &\sum_{i=0}^{n}\sum_{j=0}^{i} a_ia_j = \frac{1}{2}\left ( \left ( \sum_{i=0}^{n}a_i \right )^2 + \left ( \sum_{i=0}^{n}a_i^2 \right )\right ) \end{align*}$
dd
asked
in
Combinatory
Feb 25, 2017
by
dd
550
views
discrete-mathematics
summation
2
votes
0
answers
27
summation series
what is the summation of this series? S=nC0*20+nC1*21+nC2*22+..............nCn*2n
firki lama
asked
in
Combinatory
Jan 17, 2017
by
firki lama
338
views
summation
5
votes
4
answers
28
Time complexity and output
#include <stdio.h> #define N 3 int main() { int array[N] = {1,2,3}; int i,j; for ( i=1; i<(1<<N); i++) { for( j=0; j<N; j++) { if((1<<j)&i) { printf("%d", array[j]); } } printf("\n"); } return 0 ... $N = n \;\; , n \; \text{ is a positive integer }$ ? B. What is the output? C. What will be the complexity when $N$ is large.
dd
asked
in
Programming
Dec 17, 2016
by
dd
1.3k
views
time-complexity
bitwise
programming-in-c
combinatory
summation
sub-set
binomial-theorem
0
votes
1
answer
29
summation
5 digit numbers are possible from digits 1, 2, 3, 4, 5, 6, 7 When each digit is distinct is 7P5 . what is sum of all such numbers?
Neal Caffery
asked
in
Combinatory
Dec 11, 2016
by
Neal Caffery
285
views
summation
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