Infinite sums and products 2 (#10)

Calculus Level 4

Find the sum.

$1 - \frac {1}{3^3} + \frac {1}{5^3} - \frac {1}{7^3} + \frac {1}{9^3} - \ldots$

Note: Round to two decimals.

1 solution

First Last
Nov 16, 2017

The Dirichlet Beta Function is defined as: $\displaystyle\beta(n)=\sum_{k=0}^\infty\frac{(-1)^k}{(2k+1)^n}$

The problem requires $\beta(3)=\frac{\pi^3}{32}\approx.9689$ .