It is given that $\frac{1}{{{1^4}}} + \frac{1}{{{2^4}}} + \frac{1}{{{3^4}}} + ... + {\rm{to}}\;\infty = \frac{{{\pi ^4}}}{{90}}$. Then, $\frac{1}{{{1^4}}} + \frac{1}{{{3^4}}} + \frac{1}{{{5^4}}} + ...\infty $ is equal to

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Application +4 | -1

It is given that

\frac{1}{{{1^4}}} + \frac{1}{{{2^4}}} + \frac{1}{{{3^4}}} + ... + \mathrm{to}\;\infty = \frac{{{\pi ^4}}}{{90}}

. Then,

\frac{1}{{{1^4}}} + \frac{1}{{{3^4}}} + \frac{1}{{{5^4}}} + ...\infty

is equal to

View answer and explanation

Correct option: A

\frac{{{\pi ^4}}}{{96}}

Option A (

\frac{{{\pi ^4}}}{{96}}

) is correct because it is derived by subtracting the sum of even terms from the total sum of the series.

Practice All Chapter MCQs →

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

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A-(B \cap C)

(B \cup C)-A

a,b,c

a,x,b

b,y,c

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

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y=x-2

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

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

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

A P

a, b

G P

a, b, c

\frac{3}{4}