Dark Mode

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 ?

Swarnava Bose asked in Quantitative Aptitude Jul 23, 2023

by Swarnava Bose

519 views

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.

dd asked in Combinatory Jun 8, 2020

by dd

1.2k views

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

Arjun asked in Quantitative Aptitude Sep 23, 2019

by Arjun

667 views

1 vote

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

Arjun asked in Combinatory Sep 23, 2019

by Arjun

647 views

1 vote

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

Arjun asked in Quantitative Aptitude Sep 23, 2019

by Arjun

480 views

1 vote

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 $-1$ $0$ $1$ $2^n$

Arjun asked in Combinatory Sep 23, 2019

by Arjun

642 views

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

Arjun asked in Quantitative Aptitude Sep 23, 2019

by Arjun

504 views

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

Arjun asked in Quantitative Aptitude Sep 23, 2019

by Arjun

597 views

1 vote

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

Arjun asked in Others Sep 23, 2019

by Arjun

738 views

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

Arjun asked in Calculus Sep 23, 2019

by Arjun

499 views

1 vote

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

Arjun asked in Others Sep 23, 2019

by Arjun

429 views

1 vote

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

gatecse asked in Quantitative Aptitude Sep 18, 2019

567 views

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

gatecse asked in Quantitative Aptitude Sep 18, 2019

366 views

1 vote

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

gatecse asked in Quantitative Aptitude Sep 18, 2019

632 views

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

gatecse asked in Quantitative Aptitude Sep 18, 2019

265 views

1 vote

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

gatecse asked in Quantitative Aptitude Sep 18, 2019

393 views

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

gatecse asked in Quantitative Aptitude Sep 18, 2019

540 views

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

gatecse asked in Quantitative Aptitude Sep 18, 2019

386 views

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

gatecse asked in Quantitative Aptitude Sep 18, 2019

377 views

2 votes

1 answer

20

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

426 views

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 $B^2 =1$ $B^2 =0$ $B^2 =A$ $B^2 =B$

go_editor asked in Linear Algebra Sep 13, 2018

288 views

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 $a \in [-1, 1)$ $a \in (-1, 1]$ $a \in [-1, 1]$ $a \in (-\infty, \infty)$

go_editor asked in Others Sep 13, 2018

243 views

2 votes

1 answer

23

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

pankaj_vir asked in Quantitative Aptitude Aug 8, 2018

1.3k views

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?

Ayush Upadhyaya asked in Algorithms May 11, 2018

by Ayush Upadhyaya

1.1k views

1 vote

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

A_i_$_h asked in Quantitative Aptitude Sep 12, 2017

1.4k views

5 votes

1 answer

26

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

dd asked in Set Theory & Algebra Jun 11, 2017

by dd

805 views

3 votes

2 answers

27

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

dd asked in Combinatory Feb 25, 2017

by dd

820 views

2 votes

0 answers

28

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

436 views

Page:

Recent questions tagged summation