If \[\frac{1}{{{1}^{4}}}+\frac{1}{{{2}^{4}}}+\frac{1}{{{3}^{4}}}+.....+\infty =\frac{{{\pi }^{4}}}{90}\], then the value of \[\frac{1}{{{1}^{4}}}+\frac{1}{{{3}^{4}}}+\frac{1}{{{5}^{4}}}+.....\infty \]is [AMU 2005]

If \[\frac{1}{{{1}^{4}}}+\frac{1}{{{2}^{4}}}+\frac{1}{{{3}^{4}}}+.....

1.	If \[\frac{1}{{{1}^{4}}}+\frac{1}{{{2}^{4}}}+\frac{1}{{{3}^{4}}}+.....+\infty =\frac{{{\pi }^{4}}}{90}\], then the value of \[\frac{1}{{{1}^{4}}}+\frac{1}{{{3}^{4}}}+\frac{1}{{{5}^{4}}}+.....\infty \]is [AMU 2005]
A.	\[\frac{{{\pi }^{4}}}{96}\]
B.	\[\frac{{{\pi }^{4}}}{45}\]
C.	\[\frac{89}{90}{{\pi }^{4}}\]
D.	None of these
Answer» B. \[\frac{{{\pi }^{4}}}{45}\]

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If \[\frac{1}{{{1}^{4}}}+\frac{1}{{{2}^{4}}}+\frac{1}{{{3}^{4}}}+.....+\infty =\frac{{{\pi }^{4}}}{90}\], then the value of \[\frac{1}{{{1}^{4}}}+\frac{1}{{{3}^{4}}}+\frac{1}{{{5}^{4}}}+.....\infty \]is [AMU 2005]

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