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

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

If $S_{n}=\frac{1}{6}\;n\;(2n^2+9n+13)\;$ , then $\sum_{r=1}^n\;\sqrt{a_{r}}\;$ equals.

asked Jan 20, 2014 by yamini.v

1 answer

Sum of series $\;\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+.....\;is:$

asked Jan 20, 2014 by yamini.v

1 answer

If $f\;(xy)=f\;(x+y)\;\forall\;x,y\;\in\;R$ and $\;f\;(2009)=2009$ , then $f\;(-2009)$ equals

asked Jan 20, 2014 by yamini.v

1 answer

Sum of n terms of series $\;\frac{1}{1^3}\;+\frac{1+2}{1^3+2^3}\;+\frac{1+2+3}{1^3+2^3+3^3}\;+....\;is$

asked Jan 20, 2014 by yamini.v

1 answer

If x, y, z > 1 are in GP, then $\frac{1}{1+lnx}$ , $\frac{1}{lny}$ , $\frac{1}{lnz}$ are in

asked Jan 20, 2014 by yamini.v

1 answer

If in an AP , $\;m^{th}$ term is $\;\frac{1}{n}$ and $\;n^{th}\;term\;is\frac{1}{m}$ , then $\;mn^{th}$ term is :

asked Jan 20, 2014 by yamini.v

1 answer

Let $S_{1}, S_{2}$ ....be the squares such that for each $n\geq\;1$ , the length of side of $S_{n}$ = length of diagonal of $S_{n+1}$ . If side of $S_{1}$ is 20 cm, the smallest value of n such that area of $S_{n}\;<\;2$ is

asked Jan 20, 2014 by yamini.v

1 answer

If $a, b, c$ are in AP and $a^2$ , $b^2$ , $c^2$ in GP, and $a+b+c=\frac{3}{2}$ , then value of $c$ is

asked Jan 20, 2014 by yamini.v

1 answer

If $(1+3+5+....+p)$ + $(1+3+5+....+q)$ = the smallest value of $p+q+r, (p>6)$ is

asked Jan 20, 2014 by yamini.v

1 answer

Sum of series $S$ = $\frac{1}{2}$ + $\frac{1}{3}\;(1+2)$ + $\frac{1}{4}\;(1+2+3)$ + $\frac{1}{5}\;(1+2+3+4)$ +......upto 20 terms is

asked Jan 20, 2014 by yamini.v

1 answer

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