Are you familiar with this series?

Calculus Level 4

\[ \large 1 - \dfrac{1}{4} + \dfrac{1}{9} - \dfrac{1}{16} + \cdots = \, ? \]

\[\dfrac{\pi^2}{8}\] \[\ln 2\] \[\dfrac{\pi^2}{24}\] \[\dfrac{\pi^2}{6}\] \[\dfrac{\pi^2}{4}\] \[\dfrac{\pi^2}{12}\] None of these