Recent questions tagged sequence-series

$\text{5 16 49 104 181}$ __________$271$$298$$280$$281$

$\text{14, 28, 20, 40, 32, 64, _________}$$52$$56$$96$$128$

Complete the following series.$\text{4, 27, 256, 3125, ______}$$46656$$6250$$800000$$1024$

Let $\left \{ f_{n} \right \}^{\infty }_{n=1}$ be the sequence of functions on $\mathbb{R}$ defined by $f_{n}\left ( x \right )=n^{2}x^{n}.$. Let $A$ be the set of all po...

The value of the series $\sum _{n=1}^{\infty }\frac{n}{2^{n}}$ is$1$$2$$3$$4$.

Consider the sequences $\left \{ a_{n}\right \}_{n=1}^{\infty }$ and $\left \{ b_{n}\right \}_{n=1}^{\infty }$ defined by $a_...

Let $f\left ( x \right )=\frac{log\left ( 2+x \right )}{\sqrt{1+x}}$ for $x\geq 0$, and $a_{m}=\frac{1}{m}\int_{0}^{m}f\left ( t \right )dt$ for every positive integer $m...

Find the next term in the sequence$: 15O, 19S, 21U,\_\_\_\_\_?$$25Y$$23W$$25W$$23Y$

Evaluate the sum $S=1+1+\dfrac{3}{2^{2}}+\dfrac{3}{2^{3}}+\dfrac{5}{2^{4}}+\dots$$1$$2$$3$$4$

The $5000$th term of the sequence $1,2,2, 3,3,3,4,4,4,4, \cdots$ is$98$$99$$100$$101$

The sequence $\dfrac{1}{\log_{3} 2},\dfrac{1}{\log_{6} 2},\dfrac{1}{\log_{12} 2},\dfrac{1}{\log_{24} 2}\cdots$ is inArithmetic progression (AP)Geometric progression (GP)H...

The $5000$th term of the sequence $1,2,2,3,3,3,4,4,4,4,\cdots$ is$98$$99$$100$$101$

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 ...

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

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 inte...

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 $1$...

Determine the value of $'P'$ in the equation:$$P=\sqrt{20+\sqrt{20+\sqrt{20+ \sqrt{20+ \dots + \infty}}}}$$$4$$5$$10$$20$

Look at this series: $25, 25, 37, 37, \dots , 51, ….$. What number should fill the blank?$51$$39$$23$$25$

Look at this sequence $SCD\;\; TEF\;\; UGH \_\_\_\_WKL,$ and find the missing sequence.$CMN$$UJI$$VIJ$$IJT$

Look at this series: $5000, 1001, 201, 41, \dots$ What number should come next?$9$$10$$11$$42$