Let be a real number

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Let

m

be a real number. Consider the series

\sum_{n=1}^{\infty}(-1)^n\frac{n^{\,2}}{n^{\,3}+m}.\;

Determine all real values of

m

for which the alternating series error bound can be used to estimate the sum of this series beginning with

n=1