Write:

\displaystyle \sum_{n = 1}^\infty \frac 1 {n^k} = \zeta(k) for k > 1

Show that:

\displaystyle \sum_{k = 1}^\infty \frac {\zeta(2k)} {4^k} = \frac 1 2

Write:

\displaystyle \sum_{n = 1}^\infty \frac 1 {n^k} = \zeta(k) for k > 1

Show that:

\displaystyle \sum_{k = 1}^\infty \frac {\zeta(2k)} {4^k} = \frac 1 2

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