Mathematical Methods in the Physical Sciences · Problem 4.8

INFINITE SERIES, POWER SERIES — Mary Boas

Mathematics — Methods · convergent-divergent-series

Problem

Select some

\epsilon

's and find the corresponding

N

's for the series

\displaystyle\sum_{n=2}^{\infty} \frac{1}{n^2-1}

. Hint: Compare

\displaystyle\sum_{n=2}^{\infty} \frac{1}{n(n-1)} = \sum_{n=1}^{\infty} \frac{1}{n(n+1)}