Well known series with a twist

Calculus Level 4

What is $\sum_{i=-\infty}^{\infty} \frac{1}{i^2}$ ?

\frac{\pi^2}{6}

\frac{\pi^2}{3}

0

Undefined

\frac{\pi^2}{12}

1 solution

Alex Li
Jul 9, 2015

Note that one of the terms is $\frac{1}{0^2}$ .

So? Another term is $\dfrac{1}{\infty^2}$ , thus forming $\dfrac{1}{\infty^20^2}$ , which can be anything.

Kishore S. Shenoy - 5 years, 8 months ago