Mathematical Methods in the Physical Sciences · Problem 6.37

INFINITE SERIES, POWER SERIES — Mary Boas

Mathematics — Methods · special-comparison-test

Problem

Prove the special comparison test. Hint (part a): If

a_n/b_n \to L

and

M > L

, then

a_n < Mb_n

for large

n

. Compare

\displaystyle\sum_{n=1}^{\infty} a_n

with

\displaystyle\sum_{n=1}^{\infty} Mb_n