List the three conditions a function must satisfy on so that one may compare the…

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

Problem

List the three conditions a function

f(x)

must satisfy on

[1,\infty)

so that one may compare the infinite series

\sum_{n=1}^{\infty} f(n)

with the improper integral

\displaystyle \int_{1}^{\infty} f(x)\,dx

when deciding convergence.