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If $\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + \dots$ upto $\infty = \frac{π^{2}}{6}$ , then value of $\frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}} + \dots$ up to $\infty$ is

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π24

π26

π28

π212

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Correct option is C

We have 112+132+152+⋯ upto ∞ =112+122+132+142+152+162⋯ upto ∞ −1221+122+132+⋯=π26−14π26=π28

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If 112+122+132+⋯ upto ∞=π26, then value of 112+132+152+⋯up to ∞ is

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If $\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + \dots$ upto $\infty = \frac{π^{2}}{6}$ , then value of $\frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}} + \dots$ up to $\infty$ is