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if 1/1^2 + 1/2^2 +1/3^2 +....infinity.= (pi)^2/6 then 1/1^2 + 1/3^2 + 1/5^2 +.....+ =?

  1. if 1/1^2 + 1/2^2 +1/3^2 +....infinity.= (pi)^2/6 then 1/1^2 + 1/3^2 + 1/5^2 +.....+ =?

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Grade:12

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
5 years ago
\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + ..... \infty = (\frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}+....\infty) + 0.25(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+ .... \infty)

as every thing goes to infinity we can subtract the two sequences
and we get
(\frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}+....\infty) = 0.75(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+ .... \infty) = \frac{3\pi^{2/6}}{4}

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