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Division of a Polynomial by a Polynomial

If 1/12+1/2...

Question

If $\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . . u p t o \infty = \frac{π^{2}}{6}$ , then find

$\frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}} + . . . . u p t o \infty$

A

\frac{π^{2}}{6}

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B

\frac{π^{2}}{12}

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C

\frac{π^{2}}{8}

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D

none of these

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Solution

The correct option is C $\frac{π^{2}}{8}$

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Similar questions

\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . . .

\infty = \frac{π^{2}}{6},

\frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}} + . . . . =

\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . . u p t o \infty = \frac{π^{2}}{6}

, then value of

\frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}} + . . . . . u p t o \infty

\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}}

+ .......... upto

\infty = \frac{π^{2}}{6}

\frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}}

+ ........... = .......... .

\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} \dots \dots

\infty = \frac{π^{2}}{6}

\frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}} + \dots \dots =

\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . . . +

\infty = \frac{π^{2}}{6}

, then value of

\frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}} + . . . . . .

\infty

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