State the three conditions on a function defined for that must be verified before one…

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

Problem

State the three conditions on a function

f(x)

defined for

x\ge 1

that must be verified before one may compare

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

with the improper integral

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

for the purpose of determining convergence.