If 1-12-1-22-1-32-2-6- then 1-12-1-32-1-52- equals

The correct option is D π^2/8 1/1^2 + 1/3^2 + 1/5^2 + 1/7^2 +... = (1/1^2 + 1/2^2 + 1/3^2 + 1/4^2 + 1/5^2 + 1/6^2 + 1/7^2+...) (1/2^2 + 1/4^2 + 1/6^2+...) = ...

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Byju's Answer

Standard XII

Mathematics

How to Find the Inverse of a Function

If 1/12+1/22+...

Question

If $\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . \infty = \frac{π^{2}}{6}$ , then $\frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}} +$ .... equals

$\frac{π^{2}}{8}$

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$\frac{π^{2}}{12}$

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$\frac{π^{2}}{3}$

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$\frac{π^{2}}{2}$

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Solution

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

$\frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}} + \frac{1}{7^{2}} + . . .$

$= (\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + \frac{1}{4^{2}} + \frac{1}{5^{2}} + \frac{1}{6^{2}} + \frac{1}{7^{2}} + . . .) - (\frac{1}{2^{2}} + \frac{1}{4^{2}} + \frac{1}{6^{2}} + . . .)$

$= \frac{π^{2}}{6} - \frac{1}{4} (\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . .)$

$= \frac{π^{6}}{6} - \frac{1}{4} (\frac{π^{2}}{6})$

$= \frac{π^{2}}{8}$

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Similar questions

Q. If

\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + \frac{1}{4^{2}} + . . . . \infty = \frac{π^{2}}{6}

then,

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

is equal to

Q. If

\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . \infty = \frac{π^{2}}{6}

, then

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

Q. if

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

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

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

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

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upto

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

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If 112+122+132+...∞=π26, then 112+132+152+.... equals

The correct option is A π28 112+132+152+172+... =(112+122+132+142+152+162+172+...)−(122+142+162+...) =π26−14(112+122+132+...) =π66−14(π26) =π28

If $\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . \infty = \frac{π^{2}}{6}$ , then $\frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}} +$ .... equals