Mathematical Methods in the Physical Sciences · Problem 6.5

INFINITE SERIES, POWER SERIES — Mary Boas

Mathematics — Methods · comparison-test

Problem

Test the following series for convergence using the comparison test. (a)

\displaystyle\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}}

Hint: Which is larger,

n

\sqrt{n}

? (b)

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