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Recent questions tagged sequences-and-series

$\alpha$ & $\beta\;$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 .

asked 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

asked 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)$)

asked Jan 22, 2014 by yamini.v

1 answer

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

asked 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 :

asked 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 ,

asked 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

asked 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 :

asked Jan 22, 2014 by yamini.v

1 answer

If a,b,c,d are positive real number , then least value of $\;(a+b+c+d)\;(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d})\;$ is :

asked Jan 22, 2014 by yamini.v

1 answer

Ratio of sum of n terms of two AP's is $\;(5n+3)\;:\;(3n+4)\;,$ then the ratio of $\;15^{th}\;$ term will be :

asked Jan 22, 2014 by yamini.v

1 answer

Sum of first $n$ terms of an $AP$ is $kn^2$, sum of their squares will be

asked Jan 22, 2014 by yamini.v

1 answer

If $\;p=1+\frac{1}{2}+\frac{1}{3}+\;....\;+\frac{1}{n}\;$ then $\;S=\frac{1^2}{1^3}+\frac{1^2+2^2}{1^3+2^3}+\large\frac{1^2+2^2+3^2}{1^3+2^3+3^3}+\;....\;$ upto n terms equal to

asked Jan 22, 2014 by yamini.v

0 answers

If $p$ = $1$ + $\large\frac{1}{2}$ + $\large\frac{1}{3}$+....+$\large\frac{1}{n}$, then $S$ = $\large\frac{1^2}{1^3}$ + $\frac{1^2+2^2}{1^3+2^3}$ + $\large\frac{1^2+2^2+3^2}{1^3+2^3+3^3}$+.... upto $n$ terms equal to

asked Jan 22, 2014 by yamini.v

1 answer

Sum of n terms of series $(n^2-1^2)$ + $2\;.(n^2-2^2)$ + $3\;.(n^2-3^2)$+.....is

asked Jan 22, 2014 by yamini.v

1 answer

Sum of n terms of series $\;1.3.5+3.5.7+5.7.9+$.......is

asked Jan 22, 2014 by yamini.v

1 answer

Three positive numbers $p, q, r$ are in HP, $(r > p)$, then $log (p+r) + log (p-2q+r)$ is equal to

asked Jan 22, 2014 by yamini.v

1 answer

Find $\frac{1}{3}+\frac{1}{15}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}$ +....upto n terms

asked Jan 21, 2014 by yamini.v

1 answer

If $1$, $log_{b}^{a}$, $log_{c}^{b}$, $-15\;log_{a}^{c}$ are in AP, then

asked Jan 21, 2014 by yamini.v

1 answer

$p, q, r$ are three unequal numbers in AP. If $q-p$, $r-q$ and $p$ are in GP, the $p\;:\;q\;:\;r$ equals

asked Jan 21, 2014 by yamini.v

1 answer

For an AP with first term a and sum of first m terms 0, the sum of next n terms will be

asked Jan 21, 2014 by yamini.v

1 answer

If p, q, r are in increasing AP, then common difference will be

asked Jan 21, 2014 by yamini.v

1 answer

If the numbers $a, b, c, d, e$ are in AP, the value of $a-4b+6c-4d+e$ is

asked Jan 21, 2014 by yamini.v

1 answer

Sum of 20 terms of the series 1+2+3+4+5+8+7+16+9+....... is

asked Jan 21, 2014 by yamini.v

1 answer

The sum $1+\frac{3}{x}+\frac{9}{x^2}+\frac{27}{x^3}+....\infty$, ($x\neq\;0$) is finite if

asked Jan 21, 2014 by yamini.v

1 answer

If the numbers $\;1,x^2,6-x^2\;$ are in GP , then value of $x$ is :

asked Jan 21, 2014 by yamini.v

1 answer

If 20 is divided into four parts which are in AP such that ratio of product of first and fourth part and product of second and third part is 2:3, then the largest part is

asked Jan 21, 2014 by yamini.v

1 answer

$\displaystyle\sum_{r=1}^{n}\;\frac{r}{(r+1)!}=$

asked Jan 21, 2014 by yamini.v

1 answer

Sum of $\;\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+\frac{1}{3.4.5.6}+\;.....\;upto\;\infty\;is$

asked Jan 21, 2014 by yamini.v

1 answer

If $j,k,l$ are in AP $p,q,r$ in HP and $jp,kq,lr$ in $GP$ , then $\;\frac{p}{r}+\frac{r}{p}\;is\;equal\;to:$

asked Jan 21, 2014 by yamini.v

1 answer

Let $\;a_{r}=\int\limits_{0}^{\frac{\pi}{4}}\;tan^{r}\;x\;dx$ , then $\;a_{1}+a_{3}\;,a_{2}+a_{4}\;,a_{3}+a_{5}\;$ are in

asked Jan 21, 2014 by yamini.v

1 answer

$(1-2y)\;(1+3x+9x^2+27x^3+81x^4+243x^5+729x^6)$ = $(1-64y^6)$, $(y\;\neq\;1)$, then $\frac{x}{y}$ is

asked Jan 21, 2014 by yamini.v

1 answer

Let $a_{1}+a_{2}+a_{3}+\;......$ be terms of an AP. If $\;\frac{S_{p}}{S_{q}}=\frac{p^2}{q^2}\;then\;\frac{a_{7}}{a_{14}} =$

asked Jan 21, 2014 by yamini.v

1 answer

If $l,m,n$ are $\;x^{th}\;,y^{th}\;and\;z^{th}$ term of a GP then , $\begin{vmatrix}\log l& x & 1\\\log m &y &1\\\log n &z &1\end{vmatrix}=$

asked Jan 21, 2014 by yamini.v

1 answer

If first and last term of an AP are $a$ & $l$ and sum of all terms is $s$, then common difference is

asked Jan 21, 2014 by yamini.v

1 answer

Sum of $n$ terms of AP is $6n^2+5n$ while $a_{m}=164$, the value of $m$ is

asked Jan 21, 2014 by yamini.v

1 answer

Let $S=\frac{3}{19}+\frac{33}{(19)^2}+\frac{333}{(19)^3}+$......$\infty$. Find $S$.

asked Jan 21, 2014 by yamini.v

1 answer

Harmonic mean of roots of equation $(5+\sqrt{2})\;x^2$ - $(4+\sqrt{2})\;x$ + $8$ + $2\;\sqrt{2}$ will be

asked Jan 21, 2014 by yamini.v

1 answer

Natural numbers are divided into groups $\;(1)\;,\;(2,3,4)\;,\;(5,6,7,8,9)\;.....$ Sum of first and last term of $n^{th}\;$ group will be :

asked Jan 21, 2014 by yamini.v

1 answer

If in an AP $m$ times $\;m^{th}\;$ term equals $n$ times $\;n^{th}$ term , then $\;(m+n)^{th}$ term will be

asked Jan 21, 2014 by yamini.v

1 answer

Let $a_{n}\;$ be $\;n^{th}$ term of AP. If $\;\displaystyle\sum_{r=1}^{50}\;a_{2r}=p\;and \;\displaystyle\sum_{r=1}^{50}\;a_{2r-1}=q\;$ the common difference is :

asked Jan 21, 2014 by yamini.v

1 answer

If $\;x=\sqrt{2+\sqrt{2+\sqrt{2+------\;\infty}}}\;and\;y=\sqrt{2\;\sqrt{2\;\sqrt{2\;\sqrt{2\;----\;\infty}}}}$ then $xy$ equals

asked Jan 20, 2014 by yamini.v

1 answer

Sum of series $\;S=\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\;....\;+\frac{1}{100\sqrt{99}+99\sqrt{100}} \;is$

asked Jan 20, 2014 by yamini.v

1 answer

If $1^4+2^4+3^4+.....n^4$ = $an^5+bn^4+cn^3+dn^2+en+f$, find $a$

asked Jan 20, 2014 by yamini.v

1 answer

Sum of series $(n)(n)$ + $(n-1)(n+1)$ + $(n-2)(n+2)$ +....+ $1\;(2n-1)$ is

asked Jan 20, 2014 by yamini.v

1 answer

Sum of series $\;\sum_{r=1}^{n}\;r\;log\;\frac{r+1}{r}$ is :

asked Jan 20, 2014 by yamini.v

1 answer

If $a_{1},a_{2},...a_{n}$ are in HP. , Then $\;a_{1}a_{2}+a_{2}a_{3}+.....+a_{n}\;a_{n-1}$ is equal to

asked Jan 20, 2014 by yamini.v

1 answer

Sum of $n$ terms of series $S$ = $1$ + $2 \;(1+\frac{1}{n})$ + $3(1+\frac{1}{n})^2$ + ....is given by

asked Jan 20, 2014 by yamini.v

1 answer

For $0\;<\;x\;<\;\pi$, the values of x which satisfies $1+|cos\;x|+|cos\;x|^2+|cos\;x|^3+$....$\infty$ = $2^4$ are

asked Jan 20, 2014 by yamini.v

1 answer

If $f\;(x)$ is a two degree polynomial such that $f\;(3)=f\;(-3)$ and $a, b, c$ are in $AP$, then $f'(a)$, $f'(b)$ and $f'(c)$ are in

asked Jan 20, 2014 by yamini.v

1 answer

If $\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+$......upto $\infty$ = $\frac{\phi^2}{g}$, then $\frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}+$.....upto $\infty$ will be

asked Jan 20, 2014 by yamini.v

1 answer

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