Recent questions tagged summation

+1 vote

2 answers

1

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

asked Sep 23, 2019 in Numerical Ability by Arjun Veteran (430k points) | 83 views

+1 vote

1 answer

2

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 $3^{n+1}+2^{n+1}$ $3^n \times 2^n$ $3^n + 2^n$ $2 \times 3^n$

asked Sep 23, 2019 in Combinatory by Arjun Veteran (430k points) | 48 views

+1 vote

0 answers

3

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 $\frac{\pi}{4}$ $\frac{\pi}{8}$ $\frac{\pi}{6}$ $2 \pi$

asked Sep 23, 2019 in Numerical Ability by Arjun Veteran (430k points) | 51 views

+1 vote

1 answer

4

ISI2014-DCG-72
The sum $\sum_{k=1}^n (-1)^k \:\: {}^nC_k \sum_{j=0}^k (-1)^j \: \: {}^kC_j$ is equal to $-1$ $0$ $1$ $2^n$

asked Sep 23, 2019 in Combinatory by Arjun Veteran (430k points) | 37 views

+1 vote

1 answer

5

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

asked Sep 23, 2019 in Numerical Ability by Arjun Veteran (430k points) | 24 views

0 votes

1 answer

6

ISI2015-MMA-24
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 by Arjun Veteran (430k points) | 19 views

+1 vote

1 answer

7

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 $\log \frac{1+x}{1-x}$ $\frac{x}{1-x} + \log(1+x)$ $\frac{1}{1-x} + \log(1-x)$ $\frac{x}{1-x} + \log(1-x)$

asked Sep 23, 2019 in Others by Arjun Veteran (430k points) | 20 views

0 votes

0 answers

8

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 $\log_e \frac{\beta}{\alpha}$ $\log_e \frac{1+ \beta}{1 + \alpha}$ $\log_e \frac{1+\alpha }{1+ \beta}$ $\infty$

asked Sep 23, 2019 in Calculus by Arjun Veteran (430k points) | 20 views

+1 vote

0 answers

9

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

asked Sep 23, 2019 in Others by Arjun Veteran (430k points) | 16 views

0 votes

2 answers

10

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

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 74 views

0 votes

1 answer

11

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

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 27 views

+1 vote

2 answers

12

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

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 52 views

0 votes

1 answer

13

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

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 20 views

0 votes

1 answer

14

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

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 18 views

0 votes

1 answer

15

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

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 33 views

0 votes

0 answers

16

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 $\frac{1}{1-x^{16}}$ $\frac{1}{1-x^{12}}$ $\frac{1}{1-x} – \frac{1}{1-x^{16}}$ $\frac{1}{1-x} – \frac{1}{1-x^{12}}$

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 18 views

0 votes

1 answer

17

ISI2018-DCG-27
$\sum_{n=1}^{\infty}\frac{1}{n(n+1)}$ is $2$ $1$ $\infty$ not a convergent series

asked Sep 18, 2019 in Numerical Ability by gatecse Boss (17.5k points) | 15 views

+2 votes

1 answer

18

Kenneth Rosen Edition 6th Exercise 2.4 Question 15c (Page No. 161)
$\sum_{j=2}^{8}(-3)^j$

asked Dec 5, 2018 in Set Theory & Algebra by aditi19 Active (5.2k points) | 74 views

+2 votes

1 answer

19

ISI2016-MMA-18
Let $A=\begin{pmatrix} -1 & 2 \\ 0 & -1 \end{pmatrix}$, and $B=A+A^2+A^3+ \dots +A^{50}$. Then $B^2 =1$ $B^2 =0$ $B^2 =A$ $B^2 =B$

asked Sep 13, 2018 in Linear Algebra by jothee Veteran (105k points) | 28 views

0 votes

0 answers

20

ISI2016-MMA-22
The infinite series $\Sigma_{n=1}^{\infty} \frac{a^n \log n}{n^2}$ converges if and only if $a \in [-1, 1)$ $a \in (-1, 1]$ $a \in [-1, 1]$ $a \in (-\infty, \infty)$

asked Sep 13, 2018 in Others by jothee Veteran (105k points) | 14 views

+1 vote

1 answer

21

Infinite series
Find the infinite sum of the series $1 + \frac{4}{7} + \frac{9}{7^2} + \frac{16}{7^3} + \frac{25}{7^4} + .............\Join$

asked Aug 8, 2018 in Numerical Ability by pankaj_vir Boss (10.7k points) | 166 views

0 votes

0 answers

22

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?

asked May 11, 2018 in Algorithms by Ayush Upadhyaya Boss (29k points) | 145 views

+1 vote

1 answer

23

addition
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 by A_i_$_h Boss (10.2k points) | 445 views

+5 votes

1 answer

24

Series Summation
Series summation of $S_n$ in closed form? $\begin{align*} &S_n = \frac{1}{1.2.3.4} + \frac{1}{2.3.4.5} + \frac{1}{3.4.5.6} + \dots + \frac{1}{n.(n+1).(n+2).(n+3)} \end{align*}$

asked Jun 11, 2017 in Set Theory & Algebra by dd Veteran (57.2k points) | 226 views

+3 votes

2 answers

25

Manipulation of sum
Prove the identity: $\begin{align*} &\sum_{i=0}^{n}\sum_{j=0}^{i} a_ia_j = \frac{1}{2}\left ( \left ( \sum_{i=0}^{n}a_i \right )^2 + \left ( \sum_{i=0}^{n}a_i^2 \right )\right ) \end{align*}$

asked Feb 25, 2017 in Combinatory by dd Veteran (57.2k points) | 172 views

+2 votes

0 answers

26

summation series
what is the summation of this series? S=nC0*20+nC1*21+nC2*22+..............nCn*2n

asked Jan 17, 2017 in Combinatory by firki lama Junior (681 points) | 108 views

+4 votes

1 answer

27

ME algo doubt

asked Jan 8, 2017 in Algorithms by Arnabi Loyal (8k points) | 141 views

+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.

asked Dec 17, 2016 in Programming by dd Veteran (57.2k points) | 633 views

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?

asked Dec 11, 2016 in Combinatory by Neal Caffery Junior (959 points) | 106 views

+15 votes

2 answers

30

ISRO2016-2
What is the sum to infinity of the series, $3+6x^{2}+9x^{4}+12x^{6}+ \dots$ given $\left | x \right |<1$ $\frac{3}{(1+x^{2})}$ $\frac{3}{(1+x^{2})^{2}}$ $\frac{3}{(1-x^{2})^{2}}$ $\frac{3}{(1-x^{2})}$

asked Jul 4, 2016 in Numerical Ability by ManojK Boss (38.6k points) | 5k views

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