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Recent questions tagged summation
+3
votes
2
answers
1
ISI2014DCG4
$\underset{n \to \infty}{\lim} \dfrac{1}{n} \bigg( \dfrac{n}{n+1} + \dfrac{n}{n+2} + \cdots + \dfrac{n}{2n} \bigg)$ is equal to $\infty$ $0$ $\log_e 2$ $1$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

92
views
isi2014dcg
calculus
limits
summation
series
+1
vote
2
answers
2
ISI2014DCG16
The sum of the series $\dfrac{1}{1.2} + \dfrac{1}{2.3}+ \cdots + \dfrac{1}{n(n+1)} + \cdots $ is $1$ $1/2$ $0$ nonexistent
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
424k
points)

45
views
isi2014dcg
numericalability
summation
series
+1
vote
1
answer
3
ISI2014DCG23
The sum of the series $\:3+11+\dots +(8n5)\:$ is $4n^2n$ $8n^2+3n$ $4n^2+4n5$ $4n^2+2$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
424k
points)

30
views
isi2014dcg
numericalability
summation
series
+1
vote
1
answer
4
ISI2014DCG34
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
in
Combinatory
by
Arjun
Veteran
(
424k
points)

33
views
isi2014dcg
permutationandcombination
binomialtheorem
summation
+1
vote
0
answers
5
ISI2014DCG65
The sum $\dfrac{n}{n^2}+\dfrac{n}{n^2+1^2}+\dfrac{n}{n^2+2^2}+ \cdots + \dfrac{n}{n^2+(n1)^2} + \cdots \cdots$ is $\frac{\pi}{4}$ $\frac{\pi}{8}$ $\frac{\pi}{6}$ $2 \pi$
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
424k
points)

39
views
isi2014dcg
numericalability
summation
series
0
votes
1
answer
6
ISI2014DCG72
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
in
Combinatory
by
Arjun
Veteran
(
424k
points)

28
views
isi2014dcg
permutationandcombination
summation
+2
votes
2
answers
7
ISI2015MMA10
The value of the infinite product $P=\frac{7}{9} \times \frac{26}{28} \times \frac{63}{65} \times \cdots \times \frac{n^31}{n^3+1} \times \cdots \text{ is }$ $1$ $2/3$ $7/3$ none of the above
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

35
views
isi2015mma
calculus
limits
summation
series
nongate
+1
vote
1
answer
8
ISI2015MMA17
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
in
Numerical Ability
by
Arjun
Veteran
(
424k
points)

16
views
isi2015mma
numericalability
summation
series
nongate
0
votes
1
answer
9
ISI2015MMA24
The series $\sum_{k=2}^{\infty} \frac{1}{k(k1)}$ converges to $1$ $1$ $0$ does not converge
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
424k
points)

14
views
isi2015mma
numbersystem
converges
summation
nongate
+1
vote
1
answer
10
ISI2015MMA54
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 $\log \frac{1+x}{1x}$ $\frac{x}{1x} + \log(1+x)$ $\frac{1}{1x} + \log(1x)$ $\frac{x}{1x} + \log(1x)$
asked
Sep 23
in
Others
by
Arjun
Veteran
(
424k
points)

11
views
isi2015mma
series
summation
nongate
0
votes
0
answers
11
ISI2015MMA80
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
in
Calculus
by
Arjun
Veteran
(
424k
points)

14
views
isi2015mma
calculus
definiteintegration
summation
nongate
+1
vote
0
answers
12
ISI2015MMA84
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
in
Others
by
Arjun
Veteran
(
424k
points)

10
views
isi2015mma
series
summation
nongate
0
votes
1
answer
13
ISI2015DCG2
Let $S=\{6, 10, 7, 13, 5, 12, 8, 11, 9\}$ and $a=\underset{x \in S}{\Sigma} (x9)^2$ & $b = \underset{x \in S}{\Sigma} (x10)^2$. Then $a <b$ $a>b$ $a=b$ None of these
asked
Sep 18
in
Verbal Ability
by
gatecse
Boss
(
16.8k
points)

35
views
isi2015dcg
numericalability
numbersystem
summation
0
votes
1
answer
14
ISI2015DCG15
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
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

20
views
isi2015dcg
numericalability
numbersystem
numberseries
summation
0
votes
2
answers
15
ISI2016DCG2
Let $S=\{6,10,7,13,5,12,8,11,9\},$ and $a=\sum_{x\in S}(x9)^{2}\:\&\: b=\sum_{x\in S}(x10)^{2}.$ Then $a<b$ $a>b$ $a=b$ None of these
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

38
views
isi2016dcg
numericalability
summation
inequality
0
votes
1
answer
16
ISI2016DCG17
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
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

9
views
isi2016dcg
numericalability
series
summation
0
votes
1
answer
17
ISI2016DCG23
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
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

12
views
isi2016dcg
numericalability
logarithms
summation
0
votes
1
answer
18
ISI2016DCG65
The value of $\sin^{2}5^{\circ}+\sin^{2}10^{\circ}+\sin^{2}15^{\circ}+\cdots+\sin^{2}90^{\circ}$ is $8$ $9$ $9.5$ None of these
asked
Sep 18
in
Geometry
by
gatecse
Boss
(
16.8k
points)

10
views
isi2016dcg
trigonometry
summation
nongate
0
votes
1
answer
19
ISI2017DCG1
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
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

17
views
isi2017dcg
numericalability
logarithms
summation
0
votes
0
answers
20
ISI2017DCG13
The value of $\dfrac{x}{1x^2} + \dfrac{x^2}{1x^4} + \dfrac{x^4}{1x^8} + \dfrac{x^8}{1x^{16}}$ is $\frac{1}{1x^{16}}$ $\frac{1}{1x^{12}}$ $\frac{1}{1x} – \frac{1}{1x^{16}}$ $\frac{1}{1x} – \frac{1}{1x^{12}}$
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

10
views
isi2017dcg
numericalability
series
summation
0
votes
1
answer
21
ISI2018DCG27
$\sum_{n=1}^{\infty}\frac{1}{n(n+1)}$ is $2$ $1$ $\infty$ not a convergent series
asked
Sep 18
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

6
views
isi2018dcg
numericalability
sequenceseries
summation
+2
votes
1
answer
22
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
(
5.1k
points)

71
views
kennethrosen
discretemathematics
settheory&algebra
sequenceseries
summation
+2
votes
1
answer
23
ISI2016MMA18
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)

18
views
isi2016mmamma
linearalgebra
matrices
summation
0
votes
0
answers
24
ISI2016MMA22
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)

10
views
isi2016mmamma
sequenceseries
converges
summation
nongate
+1
vote
1
answer
25
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
(
10.6k
points)

153
views
numericalability
summation
0
votes
0
answers
26
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
(
27.6k
points)

138
views
summation
+1
vote
1
answer
27
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
(
10.1k
points)

437
views
numericalability
summation
numberseries
+5
votes
1
answer
28
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
(
57k
points)

219
views
numbertheory
summation
discretemathematics
+3
votes
2
answers
29
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
(
57k
points)

169
views
discretemathematics
summation
+2
votes
0
answers
30
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)

101
views
summation
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