# On the Riemann-Zeta Function!

**Calculus**Level 5

\[\large{f(n) = \left( \dfrac{\zeta(2) + \zeta(3) + \ldots + \zeta(n+1)}{n} \right)^{n^\alpha}}\]

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 \(A+B\) upto three decimal places.