# Infinite series (4)

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• March 6th 2010, 03:36 PM
Miss
Quote:

Originally Posted by NonCommAlg
you should know that the convergence of $\int^{\infty} f(x) \ dx$ doesn't necessarily imply that $\sum^{\infty} f(n)$ is convergent. for example $\int_0^{\infty} \sin x^2 \ dx=\sqrt{\frac{\pi}{8}}$ but the series $\sum_{n=0}^{\infty} \sin n^2$ is divergent.

Ohh.
But the integral test said that "if and only if".
Maybe it implies the convergence only when function is positive,continuous and decreasing. Right?
• March 6th 2010, 05:19 PM
Krizalid
when i read the "maybe," then yes.
• March 11th 2010, 07:03 AM
Miss
Quote:

Originally Posted by Krizalid
when i read the "maybe," then yes.