For a series whose terms satisfy where is positive

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

Problem

For a series whose terms satisfy

a_n=f(n)

where

f

is positive, continuous, and decreasing on

[n,\infty)

, write the inequality that bounds the remainder

R_n

of the series in terms of improper integrals of

f