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Recent questions tagged summation

3 votes
1 answer
1
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.
asked Jun 8 in Combinatory dd 322 views
1 vote
2 answers
2
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
asked Sep 23, 2019 in Numerical Ability Arjun 200 views
1 vote
1 answer
3
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 $3^{n+1}+2^{n+1}$ $3^n \times 2^n$ $3^n + 2^n$ $2 \times 3^n$
asked Sep 23, 2019 in Combinatory Arjun 137 views
1 vote
0 answers
4
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 $\frac{\pi}{4}$ $\frac{\pi}{8}$ $\frac{\pi}{6}$ $2 \pi$
asked Sep 23, 2019 in Numerical Ability Arjun 117 views
1 vote
1 answer
5
The sum $\sum_{k=1}^n (-1)^k \:\: {}^nC_k \sum_{j=0}^k (-1)^j \: \: {}^kC_j$ is equal to $-1$ $0$ $1$ $2^n$
asked Sep 23, 2019 in Combinatory Arjun 95 views
1 vote
1 answer
6
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
asked Sep 23, 2019 in Numerical Ability Arjun 140 views
0 votes
1 answer
7
The series $\sum_{k=2}^{\infty} \frac{1}{k(k-1)}$ converges to $-1$ $1$ $0$ does not converge
asked Sep 23, 2019 in Numerical Ability Arjun 138 views
1 vote
1 answer
8
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 $\log \frac{1+x}{1-x}$ $\frac{x}{1-x} + \log(1+x)$ $\frac{1}{1-x} + \log(1-x)$ $\frac{x}{1-x} + \log(1-x)$
asked Sep 23, 2019 in Others Arjun 168 views
0 votes
0 answers
9
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 $\log_e \frac{\beta}{\alpha}$ $\log_e \frac{1+ \beta}{1 + \alpha}$ $\log_e \frac{1+\alpha }{1+ \beta}$ $\infty$
asked Sep 23, 2019 in Calculus Arjun 123 views
1 vote
0 answers
10
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
asked Sep 23, 2019 in Others Arjun 74 views
0 votes
2 answers
11
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
asked Sep 18, 2019 in Numerical Ability gatecse 122 views
0 votes
1 answer
12
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
asked Sep 18, 2019 in Numerical Ability gatecse 57 views
1 vote
2 answers
13
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
asked Sep 18, 2019 in Numerical Ability gatecse 102 views
0 votes
1 answer
14
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
asked Sep 18, 2019 in Numerical Ability gatecse 43 views
0 votes
1 answer
15
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
asked Sep 18, 2019 in Numerical Ability gatecse 57 views
1 vote
2 answers
16
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
asked Sep 18, 2019 in Numerical Ability gatecse 126 views
0 votes
1 answer
17
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 $\frac{1}{1-x^{16}}$ $\frac{1}{1-x^{12}}$ $\frac{1}{1-x} – \frac{1}{1-x^{16}}$ $\frac{1}{1-x} – \frac{1}{1-x^{12}}$
asked Sep 18, 2019 in Numerical Ability gatecse 96 views
0 votes
1 answer
18
$\sum_{n=1}^{\infty}\frac{1}{n(n+1)}$ is $2$ $1$ $\infty$ not a convergent series
asked Sep 18, 2019 in Numerical Ability gatecse 52 views
2 votes
1 answer
20
Let $A=\begin{pmatrix} -1 & 2 \\ 0 & -1 \end{pmatrix}$, and $B=A+A^2+A^3+ \dots +A^{50}$. Then $B^2 =1$ $B^2 =0$ $B^2 =A$ $B^2 =B$
asked Sep 13, 2018 in Linear Algebra jothee 80 views
0 votes
0 answers
21
The infinite series $\Sigma_{n=1}^{\infty} \frac{a^n \log n}{n^2}$ converges if and only if $a \in [-1, 1)$ $a \in (-1, 1]$ $a \in [-1, 1]$ $a \in (-\infty, \infty)$
asked Sep 13, 2018 in Others jothee 69 views
1 vote
1 answer
22
Find the infinite sum of the series $1 + \frac{4}{7} + \frac{9}{7^2} + \frac{16}{7^3} + \frac{25}{7^4} + .............\Join$
asked Aug 8, 2018 in Numerical Ability pankaj_vir 255 views
0 votes
0 answers
23
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?
asked May 11, 2018 in Algorithms Ayush Upadhyaya 286 views
1 vote
1 answer
24
value of 1/3 + 1/15 + 1/35 +............................+1/9999 a)100/101 b)50/101 c)100/51 d)50/51
asked Sep 12, 2017 in Numerical Ability A_i_$_h 609 views
5 votes
1 answer
25
Series summation of $S_n$ in closed form? $\begin{align*} &S_n = \frac{1}{1.2.3.4} + \frac{1}{2.3.4.5} + \frac{1}{3.4.5.6} + \dots + \frac{1}{n.(n+1).(n+2).(n+3)} \end{align*}$
asked Jun 11, 2017 in Set Theory & Algebra dd 339 views
3 votes
2 answers
26
Prove the identity: $\begin{align*} &\sum_{i=0}^{n}\sum_{j=0}^{i} a_ia_j = \frac{1}{2}\left ( \left ( \sum_{i=0}^{n}a_i \right )^2 + \left ( \sum_{i=0}^{n}a_i^2 \right )\right ) \end{align*}$
asked Feb 25, 2017 in Combinatory dd 313 views
2 votes
0 answers
27
what is the summation of this series? S=nC0*20+nC1*21+nC2*22+..............nCn*2n
asked Jan 17, 2017 in Combinatory firki lama 136 views
4 votes
1 answer
28
5 votes
4 answers
29
#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; } A. How many times the if successfully executes in ... how many time when $N = n \;\; , n \; \text{ is a positive integer }$ ? B. What is the output? C. What will be the complexity when $N$ is large.
asked Dec 17, 2016 in Programming dd 731 views
0 votes
1 answer
30
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?
asked Dec 11, 2016 in Combinatory Neal Caffery 145 views
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