Math Help - Infinite series (4)

1. 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?

2. when i read the "maybe," then yes.

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