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?


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