# 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.

×