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Recent questions tagged ch9
Questions
Sum of n terms of the series $\large\frac{1}{4}+\large\frac{7}{16}+\large\frac{37}{64}+\large\frac{175}{256}$+... is
jeemain
math
class11
ch9
sequences-and-series
difficult
sum-of-n-terms-of-special-series
q185
asked
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:
jeemain
math
class11
ch9
sequences-and-series
difficult
sum-of-n-terms-of-special-series
q184
asked
Jan 23, 2014
by
yamini.v
1
answer
$\sqcap_{n=2}^{\infty}\;\large\frac{n^3-1}{n^3+1}$ equals
jeemain
math
class11
ch9
sequences-and-series
difficult
sum-of-n-terms-of-special-series
q183
asked
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
jeemain
math
class11
ch9
sequences-and-series
difficult
sum-of-n-terms-of-special-series
q182
asked
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
jeemain
math
class11
ch9
sequences-and-series
difficult
sum-of-n-terms-of-special-series
q176
asked
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 $n\;\geq\;2$
jeemain
math
class11
ch9
sequences-and-series
difficult
sum-of-n-terms-of-special-series
q181
asked
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 $\displaystyle\sum_{n=2}^{\infty}\;\large\frac{1}{f_{n+1}\;.f_{n-1}}$
jeemain
math
class11
ch9
sequences-and-series
difficult
sum-of-n-terms-of-special-series
q180
asked
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 $\displaystyle\sum_{r=1}^{n}\;S_{r}$.
jeemain
math
class11
ch9
sequences-and-series
difficult
sum-of-n-terms-of-special-series
q179
asked
Jan 23, 2014
by
yamini.v
1
answer
Find sum upto n terms: $\large\frac{3}{1^2.2^2}+\large\frac{5}{2^2.3^2}+\large\frac{7}{3^2.4^2}$+....
jeemain
math
class11
ch9
sequences-and-series
difficult
sum-of-n-terms-of-special-series
q178
asked
Jan 23, 2014
by
yamini.v
1
answer
Find the sum of the numbers in the $n^{th}$ set: $(1)$, $(2,3)$, $(4,5,6)$, $(7,8,9,10)$.....
jeemain
math
class11
ch9
sequences-and-series
difficult
sum-of-n-terms-of-special-series
q177
asked
Jan 23, 2014
by
yamini.v
1
answer
Find sum of first n terms of series : $\;1+\large\frac{1}{1+2}+\large\frac{1}{1+2+3}+\;....$
jeemain
math
class11
ch9
sequences-and-series
difficult
sum-of-n-terms-of-special-series
q176
asked
Jan 23, 2014
by
yamini.v
1
answer
Evaluate sum to n terms $\;1.1+2.01+3.001+\;.....$
jeemain
math
class11
ch9
sequences-and-series
difficult
sum-of-n-terms-of-special-series
q175
asked
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,
jeemain
math
class11
ch9
sequences-and-series
difficult
arithmetic-progression
q174
asked
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
jeemain
math
class11
ch9
sequences-and-series
difficult
harmonic-progression
q173
asked
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
jeemain
math
class11
ch9
sequences-and-series
difficult
arithmetic-progression
q172
asked
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 :
jeemain
math
class11
ch9
sequences-and-series
difficult
sum-of-n-terms-of-special-series
q171
asked
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
jeemain
math
class11
ch9
sequences-and-series
difficult
sum-of-n-terms-of-special-series
q170
asked
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 $a$, $(a > b)$.
jeemain
math
class11
ch9
sequences-and-series
difficult
arithmetic-progression
q169
asked
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
jeemain
math
class11
ch9
sequences-and-series
difficult
geometric-progression
q168
asked
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
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q167
asked
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
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q166
asked
Jan 23, 2014
by
yamini.v
1
answer
$p\;(x)=\large\frac{1+x^2+x^4+\;...\;x^{2n-2}}{1+x+x^2+\;...\;+x^{n-1}}\;$ is a polynomial in x , then n must be
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q164
asked
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
jeemain
math
class11
ch9
sequences-and-series
medium
arithmetic-progression
q163
asked
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
jeemain
math
class11
ch9
sequences-and-series
medium
relationship-between-ap-and-gm
q162
asked
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
jeemain
math
class11
ch9
sequences-and-series
medium
relationship-between-ap-and-gm
q161
asked
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
jeemain
math
class11
ch9
sequences-and-series
medium
relationship-between-ap-and-gm
q160
asked
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
jeemain
math
class11
ch9
sequences-and-series
medium
harmonic-progression
q159
asked
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
jeemain
math
class11
ch9
sequences-and-series
medium
geometric-progression
q158
asked
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 .
jeemain
math
class11
ch9
sequences-and-series
medium
relationship-between-ap-and-gm
q157
asked
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 .
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q156
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
jeemain
math
class11
ch9
sequences-and-series
medium
relationship-between-ap-and-gm
q155
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)$)
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q154
asked
Jan 22, 2014
by
yamini.v
1
answer
If $\;a_{1}=1\;,a_{n+1}=2a_{n}+1$ then , $\;a_{n+1}$ equals
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q153
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 :
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q152
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 ,
jeemain
math
class11
ch9
sequences-and-series
medium
geometric-progression
q151
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
jeemain
math
class11
ch9
sequences-and-series
medium
relationship-between-ap-and-gm
q150
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 :
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q149
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 :
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q148
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 :
jeemain
math
class11
ch9
sequences-and-series
medium
arithmetic-progression
q147
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
jeemain
math
class11
ch9
sequences-and-series
medium
arithmetic-progression
q146
mock
asked
Jan 22, 2014
by
yamini.v
1
answer
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
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q144
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
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q143
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
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q142
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
jeemain
math
class11
ch9
sequences-and-series
medium
arithmetic-progression
q141
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
jeemain
math
class11
ch9
sequences-and-series
medium
sum-of-n-terms-of-special-series
q140
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
jeemain
math
class11
ch9
sequences-and-series
medium
arithmetic-progression
q139
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
jeemain
math
class11
ch9
sequences-and-series
medium
relationship-between-ap-and-gm
q138
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
jeemain
math
class11
ch9
sequences-and-series
medium
arithmetic-progression
q137
asked
Jan 21, 2014
by
yamini.v
1
answer
If p, q, r are in increasing AP, then common difference will be
jeemain
math
class11
ch9
sequences-and-series
medium
arithmetic-progression
q136
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
jeemain
math
class11
ch9
sequences-and-series
medium
arithmetic-progression
q135
asked
Jan 21, 2014
by
yamini.v
1
answer
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