Give an example of a continuous, non-negative function f: [1, infinity) --> R such that if an = f(n) for each positive integer n, the series [tex]\sum[/tex] an diverges, while the improper integral from 1 to infinity of f converges. Justify your answer.
The Attempt at a Solution
I have tried to randomly pick some functions I thought would work but can't seem to get one to converge and the other to diverge. For instance the series (1/n) will obviously diverge (p-test) but the integral of (1/n) will be the ln(n) which would give me an infinite value when taking the limit as n approaches infinity. Any advice on what type of function would work.