​​​​​​It is known that Σ 1/(2r-1)^2 = π^2/8; r=1,∞ , then Σ 1/r^2; r=1,∞ is

Question

It is known that \(\sum\limits_{r = 1}^\infty \frac1{(2r -1)^2} = \frac{\pi^2}8\), then \(\sum\limits_{r = 1}^\infty \frac1{r^2}\) is  

a. \(\frac{\pi^2}{24}\)

b. \(\frac{\pi^2}{3}\)

c. \(\frac{\pi^2}{6}\)

d. none of these

Answer 1

Correct option is c. \(\frac{\pi^2}{6}\)