# On the Riemann-Zeta Function!

Calculus Level 5

$\large{f(n) = \left( \dfrac{\zeta(2) + \zeta(3) + \cdots + \zeta(n+1)}{n} \right)^{n^\alpha}}$

Let $f(n)$ be a function defined as above, where $\zeta(k) = \displaystyle \sum_{p=1}^\infty \dfrac{1}{p^k}$.
Let $A = \displaystyle \lim_{n \to \infty} f(n)$, when $\alpha = 1$.
Let $B = \displaystyle \lim_{n \to \infty} f(n)$, when $\alpha = \dfrac12$.

Find the value of $A+B$ up to three decimal places.

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