Recent questions tagged sequence-series

0 votes
1 answer
1
The $5000$th term of the sequence $1,2,2, 3,3,3,4,4,4,4, \cdots$ is $98$ $99$ $100$ $101$
2 votes
1 answer
2
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
1 vote
1 answer
3
The $5000$th term of the sequence $1,2,2,3,3,3,4,4,4,4,\cdots$ is $98$ $99$ $100$ $101$
0 votes
1 answer
4
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? $n^2+4(4p+1)+4p^2-2=0$ $n^2+4(4p+1)+4p^2+2=0$ $(n-2p)^2=n+2$ $(n+2p)^2=n+2$
0 votes
1 answer
5
$\sum_{n=1}^{\infty}\frac{1}{n(n+1)}$ is $2$ $1$ $\infty$ not a convergent series
3 votes
1 answer
6
Fill in the missing value
2 votes
2 answers
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 $:$ $V$ $U$ $T$ $W$
0 votes
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8
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.
2 votes
1 answer
9
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.
1 vote
1 answer
10
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 $0$
2 votes
2 answers
11
The missing number in the given sequence $343,1331,$_____$,4913$ is $3375$ $2744$ $2197$ $4096$
0 votes
2 answers
12
If IMHO=JNIP; IDK=JEL; and SO=TP, then IDC=______ JDE JED JDC JCD
1 vote
1 answer
13
Look at this series: $25, 25, 37, 37, \dots , 51, ….$. What number should fill the blank? $51$ $39$ $23$ $25$
1 vote
1 answer
14
Look at this sequence $SCD\;\; TEF\;\; UGH \_\_\_\_WKL,$ and find the missing sequence. $CMN$ $UJI$ $VIJ$ $IJT$
1 vote
1 answer
15
Look at this series: $5000, 1001, 201, 41, \dots$ What number should come next? $9$ $10$ $11$ $42$
2 votes
1 answer
16
$\sum_{j=2}^{8}(-3)^j$
0 votes
1 answer
17
0 votes
1 answer
18
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 $p=q=r$
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19
The infinite series $\Sigma_{n=1}^{\infty} \frac{a^n \log n}{n^2}$ converges if and only if $a \in [-1, 1)$ $a \in (-1, 1]$ $a \in [-1, 1]$ $a \in (-\infty, \infty)$
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20
What is sum of the following series 1+ √2+ √3 +√4.....+√n ? Asymptotic answer will be okay too.
0 votes
0 answers
21
What is sum of the series 1+ √2+ √3 +√4.....+√n ? Assymptotic answer will be okay too.
0 votes
0 answers
22
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
2 votes
1 answer
23
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
11 votes
10 answers
24
$\text{ What is the missing number in the following sequence?}$ $2,\,12,\,60,\,240,\,720,\,1440,\,\underline{\;\;\;\;\;\;\;\;},0$ $2880$ $1440$ $720$ $0$
2 votes
1 answer
25
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
1 vote
1 answer
26
How to solve such ques? Answer is in asymptotic notation : S1 = theta (n), S2= theta (n log n)
1 vote
1 answer
27
3 votes
3 answers
28
Find the missing sequence in the letter series. $B, FH, LNP$, _______. $SUWY$ $TUVW$ $TVXZ$ $TWXZ$
1 vote
5 answers
29
15, 22, 36, 64, ?, 232
2 votes
3 answers
30
19, 23, 14, 30, 5, ?