9 Four times \(π^2/6\)

Theorem 9.1 Euler’s series: Proof 1

\[ \sum _{n\ge 1}\frac{1}{n^2} = \frac{\pi ^2}{6} \]

Proof ▶

TODO

Theorem 9.2 Euler’s series: Proof 2

\[ \sum _{k\ge 0}\frac{1}{(2 * k + 1)^2} = \frac{\pi ^2}{8} \]

Proof ▶

TODO

Theorem 9.3 Euler’s series: Proof 3

\[ \sum _{n\ge 1}\frac{1}{n^2} = \frac{\pi ^2}{6} \]

Proof ▶

TODO

Theorem 9.4 Euler’s series: Proof 4

\[ \sum _{n\ge 1}\frac{1}{n^2} = \frac{\pi ^2}{6} \]

Proof ▶

TODO

Theorem 9.5 Four proofs of Euler’s series

Collecting the proofs from the chapter

Proof ▶