Mathematical Methods in the Physical Sciences · Problem 4.7

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=1}^{\infty} \frac{1}{n^2}

. Hint:

\displaystyle\sum_{n=1}^{\infty} \frac{1}{n^2} = \sum_{n=0}^{\infty} \frac{1}{(n+1)^2}

and

\frac{1}{(n+1)^2} < \frac{1}{n(n+1)}

; use Problem 3.