If $\mathop \sum \limits_{r = 1}^\infty \frac{1}{{{{\left( {2r - 1} \right)}^2}}} = \frac{{{\pi ^2}}}{8},$ then $\mathop \sum \limits_{r = 1}^\infty \frac{1}{{{r^2}}}$ is equal to

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Hard

1 of 1

Analyzing +4 | -1

\sum \limits_{r = 1}^\infty \frac{1}{{{{\left( {2r - 1} \right)}^2}}} = \frac{{{\pi ^2}}}{8},

then

\sum \limits_{r = 1}^\infty \frac{1}{{{r^2}}}

is equal to

View answer and explanation

Correct option: C

\frac{{{\pi ^2}}}{6}

Option C (

\frac{{{\pi ^2}}}{6}

) is correct because by expressing the sum of reciprocals of all squares in terms of the sum of reciprocals of odd squares, we can find the value of the desired sum.

More Questions from SEQUENCE OF SERIES

Practice All Chapter MCQs →

Given the sets

A=\{1,2,3\}, B=\{3,4\}, C=\{4,5,6\}

, then find the following
(i)

{A} \cup({B} \cap {C})

(ii)

A-(B \cap C)

(iii)

(B \cup C)-A

a,b,c

are in A.P.;

a,x,b

are in G.P. and

b,y,c

are in G.P., then

{x^2},{b^2},{y^2}

are in Suppose

P(x)=1-x+x^2-x^3+\ldots+x^{2012}

is expressed as a polynomial in

y

, as

Q(y)=a_0+a_1 y+\ldots+a_{2012} y^{2012}

where

y=x-2

, then

\sum\limits_{{i=0}}^{2012} a_i

equals If

\log \left(\frac{5 c}{a}\right), \log \left(\frac{3 b}{5 c}\right)

and

\log \left(\frac{a}{3 b}\right)

are in

A P

, where

a, b

and c are in

G P

, then

a, b, c

are the lengths of sides of If the sum of three numbers in G.P. is 63 and the product of the first and the second term is

\frac{3}{4}

of the third term, then the numbers are If the lengths of sides of a right angled triangle are in A.P., then their ratio is