# Can we do that?

Calculus Level 5

If $\displaystyle\sum_{n=1}^{\infty}\frac{(-1)^n}{n^{0.5}}=k\times \zeta(0.5)$, find $\log_2(k+1)$.

Notation: $\zeta(\cdot)$ denote the Riemann zeta function.

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