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Recent questions tagged sequence-series

0 votes
1 answer
1
ISI2015-DCG-10
The $5000$th term of the sequence $1,2,2, 3,3,3,4,4,4,4, \cdots$ is $98$ $99$ $100$ $101$
The $5000$th term of the sequence $1,2,2, 3,3,3,4,4,4,4, \cdots$ is $98$ $99$ $100$ $101$
asked Sep 18, 2019 in Numerical Ability gatecse 60 views
2 votes
1 answer
2
ISI2016-DCG-1
The sequence $\dfrac{1}{\log_{3} 2},\dfrac{1}{\log_{6} 2},\dfrac{1}{\log_{12} 2},\dfrac{1}{\log_{24} 2}\cdots$ is in Arithmetic progression (AP) Geometric progression (GP) Harmonic progression (HP) None of these
The sequence $\dfrac{1}{\log_{3} 2},\dfrac{1}{\log_{6} 2},\dfrac{1}{\log_{12} 2},\dfrac{1}{\log_{24} 2}\cdots$ is in Arithmetic progression (AP) Geometric progression (GP) Harmonic progression (HP) None of these
asked Sep 18, 2019 in Numerical Ability gatecse 84 views
1 vote
1 answer
3
ISI2016-DCG-9
The $5000$th term of the sequence $1,2,2,3,3,3,4,4,4,4,\cdots$ is $98$ $99$ $100$ $101$
The $5000$th term of the sequence $1,2,2,3,3,3,4,4,4,4,\cdots$ is $98$ $99$ $100$ $101$
asked Sep 18, 2019 in Numerical Ability gatecse 67 views
0 votes
1 answer
4
ISI2018-DCG-3
If the co-efficient of $p^{th}, (p+1)^{th}$ and $(p+2)^{th}$ terms in the expansion of $(1+x)^n$ are in Arithmetic Progression (A.P.), then which one of the following is true? $n^2+4(4p+1)+4p^2-2=0$ $n^2+4(4p+1)+4p^2+2=0$ $(n-2p)^2=n+2$ $(n+2p)^2=n+2$
If the co-efficient of $p^{th}, (p+1)^{th}$ and $(p+2)^{th}$ terms in the expansion of $(1+x)^n$ are in Arithmetic Progression (A.P.), then which one of the following is true? $n^2+4(4p+1)+4p^2-2=0$ $n^2+4(4p+1)+4p^2+2=0$ $(n-2p)^2=n+2$ $(n+2p)^2=n+2$
asked Sep 18, 2019 in Numerical Ability gatecse 149 views
0 votes
1 answer
5
ISI2018-DCG-27
$\sum_{n=1}^{\infty}\frac{1}{n(n+1)}$ is $2$ $1$ $\infty$ not a convergent series
$\sum_{n=1}^{\infty}\frac{1}{n(n+1)}$ is $2$ $1$ $\infty$ not a convergent series
asked Sep 18, 2019 in Numerical Ability gatecse 52 views
2 votes
2 answers
7
GATE2010 MN: GA-7
Given the sequence $A,B,B,C,C,C,D,D,D,D,\ldots$ etc$.,$ that is one $A,$ two $B’s,$ three $C’s,$ four $D’s,$ five $E’s$ and so on, the $240^{th}$ latter in the sequence will be $:$ $V$ $U$ $T$ $W$
Given the sequence $A,B,B,C,C,C,D,D,D,D,\ldots$ etc$.,$ that is one $A,$ two $B’s,$ three $C’s,$ four $D’s,$ five $E’s$ and so on, the $240^{th}$ latter in the sequence will be $:$ $V$ $U$ $T$ $W$
asked May 13, 2019 in Numerical Ability Lakshman Patel RJIT 194 views
0 votes
0 answers
8
ISI2018-MMA-23
For $n\geq 1$, let $a_n=\frac{1}{2^2} + \frac{2}{3^2}+ \dots +\frac{n}{(n+1)^2}$ and $b_n=c_0 + c_1r + c_2r^2 + \dots + c_nr^n$,where $\mid c_k \mid \leq M$ for all integer $k$ and $\mid r \mid <1$. Then both $\{a_n\}$ ... $\{a_n\}$ is not a Cauchy sequence,and $\{b_n\}$ is Cauchy sequence neither $\{a_n\}$ nor $\{b_n\}$ is a Cauchy sequence.
For $n\geq 1$, let $a_n=\frac{1}{2^2} + \frac{2}{3^2}+ \dots +\frac{n}{(n+1)^2}$ and $b_n=c_0 + c_1r + c_2r^2 + \dots + c_nr^n$,where $\mid c_k \mid \leq M$ for all integer $k$ and $\mid r \mid <1$. Then both $\{a_n\}$ and $\{b_n\}$ are ... $\{b_n\}$ is not Cauchy sequence $\{a_n\}$ is not a Cauchy sequence,and $\{b_n\}$ is Cauchy sequence neither $\{a_n\}$ nor $\{b_n\}$ is a Cauchy sequence.
asked May 11, 2019 in Others akash.dinkar12 181 views
2 votes
1 answer
9
ISI-MMA 2019 Sample Questions-23
For $n \geq1$, Let $a_{n} = \frac{1}{2^{2}} + \frac{2}{3^{2}} +.....+ \frac{n}{(n+1)^{2}}$ and $b_{n} = c_{0} + c_{1}r + c_{2}r^{2}+.....+c_{n}r^{n},$ where$|c_{k}| \leq M$ for all integers $k$ ... not a Cauchy sequence (C) $\{a_n\}$ is not a Cauchy sequence but $\{b_n\}$ is a Cauchy sequence (D) neither $\{a_n\}$ nor $\{b_n\}$ is a Cauchy sequence.
For $n \geq1$, Let $a_{n} = \frac{1}{2^{2}} + \frac{2}{3^{2}} +.....+ \frac{n}{(n+1)^{2}}$ and $b_{n} = c_{0} + c_{1}r + c_{2}r^{2}+.....+c_{n}r^{n},$ where$|c_{k}| \leq M$ for all integers $k$ and $|r| \leq 1.$ ... $\{a_n\}$ is not a Cauchy sequence but $\{b_n\}$ is a Cauchy sequence (D) neither $\{a_n\}$ nor $\{b_n\}$ is a Cauchy sequence.
asked Mar 17, 2019 in Calculus ankitgupta.1729 407 views
1 vote
1 answer
10
ISI MMA-2015
Let, $a_{n} \;=\; \left ( 1-\frac{1}{\sqrt{2}} \right ) ... \left ( 1- \frac{1}{\sqrt{n+1}} \right )$ , $n \geq 1$. Then $\lim_{n\rightarrow \infty } a_{n}$ (A) equals $1$ (B) does not exist (C) equals $\frac{1}{\sqrt{\pi }}$ (D) equals $0$
Let, $a_{n} \;=\; \left ( 1-\frac{1}{\sqrt{2}} \right ) ... \left ( 1- \frac{1}{\sqrt{n+1}} \right )$ , $n \geq 1$. Then $\lim_{n\rightarrow \infty } a_{n}$ (A) equals $1$ (B) does not exist (C) equals $\frac{1}{\sqrt{\pi }}$ (D) equals $0$
asked Feb 21, 2019 in Calculus ankitgupta.1729 443 views
2 votes
2 answers
11
GATE2019 EE: GA-3
The missing number in the given sequence $343,1331,$_____$,4913$ is $3375$ $2744$ $2197$ $4096$
The missing number in the given sequence $343,1331,$_____$,4913$ is $3375$ $2744$ $2197$ $4096$
asked Feb 12, 2019 in Numerical Ability Arjun 944 views
0 votes
2 answers
12
GATE2019 ME-2: GA-3
If IMHO=JNIP; IDK=JEL; and SO=TP, then IDC=______ JDE JED JDC JCD
If IMHO=JNIP; IDK=JEL; and SO=TP, then IDC=______ JDE JED JDC JCD
asked Feb 9, 2019 in Numerical Ability Arjun 202 views
1 vote
1 answer
13
NIELIT 2018-9
Look at this series: $25, 25, 37, 37, \dots , 51, ….$. What number should fill the blank? $51$ $39$ $23$ $25$
Look at this series: $25, 25, 37, 37, \dots , 51, ….$. What number should fill the blank? $51$ $39$ $23$ $25$
asked Dec 7, 2018 in Numerical Ability Arjun 431 views
1 vote
1 answer
14
NIELIT 2018-10
Look at this sequence $SCD\;\; TEF\;\; UGH \_\_\_\_WKL,$ and find the missing sequence. $CMN$ $UJI$ $VIJ$ $IJT$
Look at this sequence $SCD\;\; TEF\;\; UGH \_\_\_\_WKL,$ and find the missing sequence. $CMN$ $UJI$ $VIJ$ $IJT$
asked Dec 7, 2018 in Numerical Ability Arjun 185 views
1 vote
1 answer
15
NIELIT 2018-11
Look at this series: $5000, 1001, 201, 41, \dots$ What number should come next? $9$ $10$ $11$ $42$
Look at this series: $5000, 1001, 201, 41, \dots$ What number should come next? $9$ $10$ $11$ $42$
asked Dec 7, 2018 in Numerical Ability Arjun 930 views
0 votes
1 answer
18
ISI2016-MMA-1
Suppose $a, b, c >0$ are in geometric progression and $a^p = b^q =c^r \neq 1$. Which one of the following is always true? $p, q, r$ are in geometric progression $p, q, r$ are in arithmetic progression $p, q, r$ are in harmonic progression $p=q=r$
Suppose $a, b, c >0$ are in geometric progression and $a^p = b^q =c^r \neq 1$. Which one of the following is always true? $p, q, r$ are in geometric progression $p, q, r$ are in arithmetic progression $p, q, r$ are in harmonic progression $p=q=r$
asked Sep 13, 2018 in Numerical Ability jothee 102 views
0 votes
0 answers
19
ISI2016-MMA-22
The infinite series $\Sigma_{n=1}^{\infty} \frac{a^n \log n}{n^2}$ converges if and only if $a \in [-1, 1)$ $a \in (-1, 1]$ $a \in [-1, 1]$ $a \in (-\infty, \infty)$
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 70 views
0 votes
0 answers
20
Find sequence's sum?
What is sum of the following series 1+ √2+ √3 +√4.....+√n ? Asymptotic answer will be okay too.
What is sum of the following series 1+ √2+ √3 +√4.....+√n ? Asymptotic answer will be okay too.
asked Sep 8, 2018 in Calculus bts1jimin 54 views
0 votes
0 answers
21
What is sum of the sequence?
What is sum of the series 1+ √2+ √3 +√4.....+√n ? Assymptotic answer will be okay too.
What is sum of the series 1+ √2+ √3 +√4.....+√n ? Assymptotic answer will be okay too.
asked Sep 8, 2018 in Calculus bts1jimin 48 views
0 votes
0 answers
22
ISI 2018 MMA 1
The number of common terms in the two sequence (3,7,11,...,407} and {2,9,16,...,70} is A)13 B)14 C)15 D)16
The number of common terms in the two sequence (3,7,11,...,407} and {2,9,16,...,70} is A)13 B)14 C)15 D)16
asked May 14, 2018 in Combinatory Tesla! 413 views
2 votes
1 answer
23
PGEE 18
If 10 and 25 are smallest numbers with multilpicative persistence of 1 and 2. What is the smallest number with multiplicative persistence of 4? 1. 77 2. Some No.'s > 77 4. None
If 10 and 25 are smallest numbers with multilpicative persistence of 1 and 2. What is the smallest number with multiplicative persistence of 4? 1. 77 2. Some No.'s > 77 4. None
asked Apr 24, 2018 in Numerical Ability Skan 271 views
11 votes
10 answers
24
GATE2018-GA-5
$\text{ What is the missing number in the following sequence?}$ $2,\,12,\,60,\,240,\,720,\,1440,\,\underline{\;\;\;\;\;\;\;\;},0$ $2880$ $1440$ $720$ $0$
$\text{ What is the missing number in the following sequence?}$ $2,\,12,\,60,\,240,\,720,\,1440,\,\underline{\;\;\;\;\;\;\;\;},0$ $2880$ $1440$ $720$ $0$
asked Feb 14, 2018 in Numerical Ability gatecse 2.5k views
2 votes
1 answer
25
Sequence
Conjecture a simple formula for an if the first few terms are 1,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4
Conjecture a simple formula for an if the first few terms are 1,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4
asked Feb 13, 2018 in Set Theory & Algebra Mk Utkarsh 135 views
1 vote
1 answer
26
Maths Sum_of_AP/GP Sum_of_AP*GP
How to solve such ques? Answer is in asymptotic notation : S1 = theta (n), S2= theta (n log n)
How to solve such ques? Answer is in asymptotic notation : S1 = theta (n), S2= theta (n log n)
asked Dec 24, 2017 in Algorithms stanchion 184 views
1 vote
1 answer
27
sequence and series
asked Nov 6, 2017 in Numerical Ability Parshu gate 593 views
3 votes
3 answers
28
GATE2016 ME-2: GA-8
Find the missing sequence in the letter series. $B, FH, LNP$, _______. $SUWY$ $TUVW$ $TVXZ$ $TWXZ$
Find the missing sequence in the letter series. $B, FH, LNP$, _______. $SUWY$ $TUVW$ $TVXZ$ $TWXZ$
asked Jan 20, 2017 in Numerical Ability makhdoom ghaya 739 views
1 vote
5 answers
29
Find the missing number. Need answer with explanation
15, 22, 36, 64, ?, 232
15, 22, 36, 64, ?, 232
asked Oct 20, 2016 in Numerical Ability jothee 1.2k views
2 votes
3 answers
30
Find the missing number. Need answer with explanation
19, 23, 14, 30, 5, ?
19, 23, 14, 30, 5, ?
asked Oct 20, 2016 in Numerical Ability jothee 802 views
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