Mathematical Methods in the Physical Sciences · Problem 20

INFINITE SERIES, POWER SERIES — Mary Boas

Mathematics — Methods · series-convergence-divergence

Problem

Test the following series for convergence or divergence:

\frac{1}{2} + \frac{1}{2^2} - \frac{1}{3} - \frac{1}{3^2} + \frac{1}{4} + \frac{1}{4^2} - \frac{1}{5} - \frac{1}{5^2} + \cdots