# Homework Help: Rate of convergeance

1. Oct 3, 2012

### gottfried

Ʃ($\frac{1}{n}$) diverges but Ʃ($\frac{1}{n^2}$) converges but both corresponding sequences converge (I think). So at what rate does a sequence have to converge for the corresponding series to converge.

Or asked differently what is the largest value x can be for Ʃ($\frac{1}{n^x}$) to diverge

2. Oct 3, 2012

### LCKurtz

The dividing line is at p = 1. $\sum \frac 1 {x^p}$ converges if $p>1$, as you can verify by the integral test.

3. Oct 3, 2012

Thanks.