Riemann Zeta Function at Even Integers/Proof 1

Lemma
We also have:

Equating the coefficients of $(1)$ with the expression given in the lemma:


 * $\zeta \left({2 n}\right) = \left({-1}\right)^{n + 1} \dfrac {B_{2 n} 2^{2 n - 1} \pi^{2 n}} {\left({2 n}\right)!}$