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Recent questions and answers in Sequence and Series

Questions >> JEEMAIN and NEET >> Mathematics >> Class11 >> Sequence and Series

In a GP, given that the first term is $ 312 ½ $ and the common ratio is $ 1/2 $ find the sum of the terms of the series to infinity.

answered May 14, 2017 by nikunjjain285

1 answer

The sum of 0.2, 0.22, 0.222, 0.2222.....till n terms is given by

answered Sep 16, 2015 by illusionist.nectar

2 answers

If $a, b, c$ are in $GP$ and equations $ax^2+2bx+c=0$ and $dx^2+2ex+f=0$ have a common root, then $\large\frac{d}{a}$, $\large\frac{e}{b}$, $\large\frac{f}{c}$ are in

answered Jan 24, 2014 by yamini.v

1 answer

If $\large\frac{a_{2}a_{3}}{a_{1}a_{4}}$ = $\large\frac{a_{2}+a_{3}}{a_{1}+a_{4}}$ = $3\;(\large\frac{a_{2}-a_{3}}{a_{1}-a_{4}})$, then, $a_{1}$, $a_{2}$, $a_{3}$, $a_{4}$ are in

answered Jan 24, 2014 by yamini.v

1 answer

If $(m+n)^{th}$, $(n+1)^{th}$, $(r+1)^{th}$ term of an AP are in GP and $m, n, r$ are in HP, then ratio of first term of AP to common difference is

answered Jan 24, 2014 by yamini.v

1 answer

$a^x=b^y=c^z=d^t$ and $a, b, c, d$ are in GP, then $x, y, z, t$ are in

answered Jan 24, 2014 by yamini.v

1 answer

If sides of $\bigtriangleup ABC \;(a, b, c)$ are in AP, $cot\;{\large\frac{c}{2}}$ equals

answered Jan 23, 2014 by yamini.v

1 answer

If AM and GM of two numbers are in ratio $p : q$, then the ratio of two numbers is

answered Jan 23, 2014 by yamini.v

1 answer

Given $\large\frac{1}{1^4}+\large\frac{1}{2^4}+\large\frac{1}{3^4}$+.....$\infty$ = $\large\frac{{\pi}^{4}}{90}$, then the value of $\large\frac{1}{1^4}+\large\frac{1}{3^4}+\large\frac{1}{5^4}$+....$\infty$ is

answered Jan 23, 2014 by yamini.v

1 answer

If $a_{1}, a_{2}, a_{3},.....$ are in HP and $f (k)$ = $\displaystyle\sum_{r=1}^{n}\;a_{r}-a_{k}$, then $\large\frac{a_{1}}{f (1)}$, $\large\frac{a_{2}}{f (2)}$, $\large\frac{a_{3}}{f (3)}$,...,$\large\frac{a_{n}}{f (n)}$ are in

answered Jan 23, 2014 by yamini.v

1 answer

$a_{1}=50$ and $a_{1}+a_{2}+....+a_{n}=n^2a_{n}$ $\forall\;n \geq 1$, value of $a_{50}$ equal to

answered Jan 23, 2014 by yamini.v

1 answer

If 1 , 3 , 8 are first three terms of an arithmetic - geometric progression (with +ve common difference ) , the sum of next three terms is :

answered Jan 23, 2014 by yamini.v

1 answer

Sum of n terms of the series $\large\frac{1}{4}+\large\frac{7}{16}+\large\frac{37}{64}+\large\frac{175}{256}$+... is

answered Jan 23, 2014 by yamini.v

1 answer

Sum of the series $\;\large\frac{2}{5}+\large\frac{3}{5^2}+\large\frac{4}{5^3}+\large\frac{2}{5^4}+\large\frac{3}{5^5}+\large\frac{4}{5^6}+...$ equals:

answered Jan 23, 2014 by yamini.v

1 answer

$\sqcap_{n=2}^{\infty}\;\large\frac{n^3-1}{n^3+1}$ equals

answered Jan 23, 2014 by yamini.v

1 answer

If $S_{n}=\large{1}{6}\;n(n+1)(n+2)$ $\forall\;n\;\geq\;1$, then $\displaystyle\lim_{n \to \infty}\;\displaystyle\sum_{r=1}^{n}\;\large\frac{1}{a_{r}}$ equals

answered Jan 23, 2014 by yamini.v

1 answer

Given $1^2+2^2+3^2+....+2003^2$ = $(2003)(4007)(334)$ and $(1)(2003)+(2)(2002)+(3)(2001)+....+(2003)(1)$ = $(2003)(334)(x)$ then value of $x$ is

answered Jan 23, 2014 by yamini.v

1 answer

If $a_{n}=\displaystyle\sum_{k=1}^{n}\;\large\frac{1}{k(n+1-k)}$, then for $n\;\geq\;2$

answered Jan 23, 2014 by yamini.v

1 answer

If $f_{1}=f_{2}=1$ and thereafter $f_{n+2}=f_{n+1}+f_{n}$ for all $n \in N$. Find $\displaystyle\sum_{n=2}^{\infty}\;\large\frac{1}{f_{n+1}\;.f_{n-1}}$

answered Jan 23, 2014 by yamini.v

1 answer

$S_{1}, S_{2},.....S_{n}$ are sums of infinite geometric series with first term $1,2,3,...n$ and common ratio $\large\frac{1}{2}$, $\large\frac{1}{3}$,...$\large\frac{1}{n+1}$ respectively. Find $\displaystyle\sum_{r=1}^{n}\;S_{r}$.

answered Jan 23, 2014 by yamini.v

1 answer

Find sum upto n terms: $\large\frac{3}{1^2.2^2}+\large\frac{5}{2^2.3^2}+\large\frac{7}{3^2.4^2}$+....

answered Jan 23, 2014 by yamini.v

1 answer

Find the sum of the numbers in the $n^{th}$ set: $(1)$, $(2,3)$, $(4,5,6)$, $(7,8,9,10)$.....

answered Jan 23, 2014 by yamini.v

1 answer

Find sum of first n terms of series : $\;1+\large\frac{1}{1+2}+\large\frac{1}{1+2+3}+\;....$

answered Jan 23, 2014 by yamini.v

1 answer

Evaluate sum to n terms $\;1.1+2.01+3.001+\;.....$

answered Jan 23, 2014 by yamini.v

1 answer

For an AP with first term $a$ and common difference $d$, if $\large\frac{S_{nx}}{S_{x}}\:(S_{r}$ denotes sum upto $r$ term$)$ is independent of $x$ then,

answered Jan 23, 2014 by yamini.v

1 answer

If $log\:_{5.2^{x}+1}^{2}$, $log\:_{2^{x-1}+1}^{4}$ and 1 are in HP, then

answered Jan 23, 2014 by yamini.v

1 answer

If the sum of first n terms of an AP is half the sum of next n terms, then $\large\frac{S_{4n}}{S_{n}}$ equals

answered Jan 23, 2014 by yamini.v

1 answer

Sum of the series $\;S=\large\frac{4}{7}-\large\frac{5}{7^2}+\large\frac{4}{7^3}-\large\frac{5}{7^4}+.....\;\infty\;$ is :

answered Jan 23, 2014 by yamini.v

1 answer

Given $a_{n}=\displaystyle\sum_{k=1}^{n}\;\sqrt{1+\large\frac{1}{k^2}+\large\frac{1}{(k+1)^2}}\;$ the value of $\;a_{5}\;$ is

answered Jan 23, 2014 by yamini.v

1 answer

$a,x,y,z,b$ are in AP such that $x+y+z=15$ and $a$, $\alpha$, $\beta$, $y$, $b$ are in HP such that $\large\frac{1}{\alpha}+\large\frac{1}{\beta}+\large\frac{1}{\gamma}=\large\frac{5}{3}$. Find $a$, $(a > b)$.

answered Jan 23, 2014 by yamini.v

1 answer

The sum of three terms of a strictly increasing GP is $\alpha S$ and sum of their squares is $S^{2}$. $\alpha^{2}$ lies in

answered Jan 23, 2014 by yamini.v

1 answer

Given for every $n \in N \;(1^2-a_{1})+(1^2-a_{2})+.......+(n^2-a_{n})=\large\frac{1}{3}n(n^2-1)\;the\;a_{n}$ equals

answered Jan 23, 2014 by yamini.v

1 answer

Given $\;t_{r}=1^2+2^2+.......\;r^2$ and $t_{1}+t_{2}+t_{3}+...\;t_{n}=\large\frac{k}{12}\;n\;(n+1)\;(n+2)\;$ the value of k will be

answered Jan 23, 2014 by yamini.v

1 answer

Four geometric means are inserted between $\;2^{9}-1\;and \;2^{9}+1\;.$ The product of these means is :

asked Jan 22, 2014 by yamini.v

0 answers

$p\;(x)=\large\frac{1+x^2+x^4+\;...\;x^{2n-2}}{1+x+x^2+\;...\;+x^{n-1}}\;$ is a polynomial in x , then n must be

answered Jan 22, 2014 by yamini.v

1 answer

If in an AP , $\;a_{n}\;$ denotes the $\;n^{th}$ term and $\;a_{p}=\frac{1}{q}$ and $\;a_{q}=\frac{1}{p}$ the root of the equation

answered Jan 22, 2014 by yamini.v

1 answer

If $\;a_{1},a_{2},\;....\;a_{n}$ are in HP then $\;\large\frac{a_{1}}{a_{2}+a_{3}+\;..\;+a_{n}}\;,\large\frac{a_{2}}{a_{1}+a_{3}+...+a_{n}}\;,\large\frac{a_{3}}{a_{1}+a_{2}+a_{4}+\;...\;+a_{n}}\;,.....\;\large\frac{a_{n}}{a_{1}+a_{2}+....+a_{n-1}}\;$ are in

answered Jan 22, 2014 by yamini.v

1 answer

If a , b , c are in AP and A.G are arithmetic and geometric mean , between a and b while $\;A^{|}\;and\;G^{|}$ are A.M and G.M between B and C . then

answered Jan 22, 2014 by yamini.v

1 answer

If $a , b , c$ are three numbers in GP . and $\;a+x\;,b+x\;,c+x\;$ are in HP then $x$ equals

answered Jan 22, 2014 by yamini.v

1 answer

If a , b , c , d are in HP $\;\large\frac{d^{-2}-a^{-2}}{c^{-2}-b^{-2}}\;$ equals

answered Jan 22, 2014 by yamini.v

1 answer

If x , y , z are in GP then , $\;\large\frac{1}{x^2-y^2}+\frac{1}{y^2}\;$ equals

answered Jan 22, 2014 by yamini.v

1 answer

For $\;n \in N \;n \geq 25$ , Let A.G.H be A.M ,G.M and H.M of 25 and n . what is the least value of n such that A.G.H are all natural numbers greater than 25 .

answered Jan 22, 2014 by yamini.v

1 answer

$\alpha$ & $\beta\;$are +ve roots of $\;x^2-2ax+ab=0\;$ then for $\;n \in N\;$$(0 \lt b \lt a)\;S_{n}=1+2(\large\frac{b}{a})$$+3(\large\frac{b}{a})^{\normalsize 2}$$+\;...+\;n$$(\large\frac{b}{a})^{n-1}\;$ can not exceed .

answered Jan 22, 2014 by yamini.v

1 answer

If a,b,c are real and $\;4a^2+9b^2+16c^2-6ab-12bc-8ac=0\;$ the a,b,c are in

answered Jan 22, 2014 by yamini.v

1 answer

$ If\;a_{1}=\frac{1}{2}\;,a_{k+1}=a_{k}^{2}+a_{k}\;\forall\;k\;\geq\;1\;and\;x_{n}=\large\frac{1}{a_{1}+1}+\large\frac{1}{a_{2}+1}+...\;\large\frac{1}{a_{n}+1}\;the \;value\;of\;[x_{50}]\;is\;([.]\;represents\;greatest\;integer\;function)$)

answered Jan 22, 2014 by yamini.v

1 answer

If $\;a_{1}=1\;,a_{n+1}=2a_{n}+1$ then , $\;a_{n+1}$ equals

answered Jan 22, 2014 by yamini.v

1 answer

Sum of n terms of series $\;S=1^2+2(2)^2+3^2+2(4)^2+5^2+\;....\;$ when n is even is :

answered Jan 22, 2014 by yamini.v

1 answer

If $\;a_{1},a_{2},a_{3}\;(a_{1}\;\geq\;0)$ are in GP with common ratio r . the value of r for which inequality $\;a_{3}\;\geq\;4a_{2}-3a_{1}$ holds is given by ,

answered Jan 22, 2014 by yamini.v

1 answer

If $\;px^2+\large\frac{q}{x}\;\geq\;r\;$ for every +ve x $\;(p>0 , q>0)\;,\;$ then $\;27pq^2\;$ can not be less than

answered Jan 22, 2014 by yamini.v

1 answer

$\;A_{1},A_{2}\;,....\;A_{n}\;$ are fixed +ve real number such that $\;A_{1}\;.A_{2}\;..\;A_{n}=k$ , then $\;A_{1}+2A_{2}+\;...\;nA_{n}$ can not be than :

answered Jan 22, 2014 by yamini.v

1 answer

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