The Riemann zeta function is defined as <br />
<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 , calculated using 1000000 as infinity.
What is Z , rounded to the nearest integer?
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The answer is 314 .
First, use iteration to calculate zeta(2). Then, multiply that value by 6, take the square root of the product, and finally multiply the result by 100.
Did the answer look familiar? It turns out that the sum of the squares of the reciprocals of the natural numbers is 6 π 2 .