## Tuesday, August 14, 2012

### Mathematics for the Liberal Arts

This problem is from Mathematics for the Liberal Arts'' (Wiley, 2012).
Leonhard Euler (1707-1783) proved the formula ${1\over 1^2} + {1\over 2^2} + {1\over 3^2} + \cdots =\frac{\pi^2}{6}.$ Can you use Euler's formula to find the exact value of $\frac{1}{1^2}-\frac{1}{2^2}+\frac{1}{3^2}-\frac{1}{4^2}+\frac{1}{5^2}-\frac{1}{6^2}+\cdots ?$