If it is given that $\frac{1}{{{1^4}}} + \frac{1}{{{2^4}}} + \frac{1}{{{3^4}}} + \ldots {\rm{to }}\infty = \frac{{{{\rm{\pi }}^4}}}{{90}},$, then the value of $\frac{1}{{{1^4}}} + \frac{1}{{{3^4}}} + \frac{1}{{{5^4}}} + \ldots {\rm{to }}\infty $ is equal to

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Application +4 | -1

If it is given that

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

, then the value of

\frac{1}{{{1^4}}} + \frac{1}{{{3^4}}} + \frac{1}{{{5^4}}} + \ldots \mathrm{to }\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 the series with even terms from the total sum.

Practice All Chapter MCQs →

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

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

A-(B \cap C)

(B \cup C)-A

a,b,c

a,x,b

b,y,c

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

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

y

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

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}