If 1-12-1-22-1-32-1-42-2-6 then 1-12-1-32-1-52- -

The correct option is C nbsp;1/1^2 + nbsp;1/3^2 + nbsp;1/5^2 + ........= nbsp;1/1^2 + nbsp;1/2^2 + nbsp;1/3^2 + ...... 1/2^2 nbsp;(1 nbsp; ...

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Byju's Answer

Standard XI

Mathematics

Proof by mathematical induction

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

Question

If $\frac{1}{1^{2}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{3^{2}}$ + $\frac{1}{4^{2}}$ + ........ = $\frac{π^{2}}{6}$ then $\frac{1}{1^{2}}$ + $\frac{1}{3^{2}}$ + $\frac{1}{5^{2}}$ + ....... =

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Solution

The correct option is C

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

$\frac{1}{1^{2}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{3^{2}}$ + ...... - $\frac{1}{2^{2}}$ $(1 + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . . . . .)$ = $\frac{π^{2}}{6}$ - $\frac{1}{4}$ $\frac{π^{2}}{6}$ = $\frac{π^{2}}{8}$

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Similar questions

Q. If

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

upto

\infty = \frac{π^{2}}{6}

, then

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

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

\infty = \frac{π^{2}}{6}

, then

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

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

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

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If 112 + 122 + 132 +142 + ........ = π26 then 112 + 132 +152 + ....... =

The correct option is C 112 + 132 + 152 + ........= 112 + 122 + 132 + ...... -122 (1+122+132+.......) = π26 - 14 π26 = π28

If $\frac{1}{1^{2}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{3^{2}}$ + $\frac{1}{4^{2}}$ + ........ = $\frac{π^{2}}{6}$ then $\frac{1}{1^{2}}$ + $\frac{1}{3^{2}}$ + $\frac{1}{5^{2}}$ + ....... =