# Estimating Zeta

**Computer Science**Level 3

The Riemann zeta function is defined as <br />

\(\zeta(s) = \sum_{n=1}^{\infty}\frac{1}{n ^ s} = \frac{1}{1 ^ s} + \frac{1}{2 ^s} + \frac{1}{3^s} + ...\) <br />

We can estimate Riemann zeta values by using large numbers in place of infinity as the upper limit of the series.

Let **Z** be an estimation of \(100\sqrt{6\zeta(2)}\), calculated using 1000000 as infinity.

What is **Z**, rounded to the nearest integer?