Infinite Sum
Source:
March 23, 2008
geometric series
Problem Statement
Let f(r) \equal{} \sum_{j \equal{} 2}^{2008} \frac {1}{j^r} \equal{} \frac {1}{2^r} \plus{} \frac {1}{3^r} \plus{} \dots \plus{} \frac {1}{2008^r}. Find \sum_{k \equal{} 2}^{\infty} f(k).