# Testing for Convergence of (Trigonometric) Series

• Apr 8th 2010, 06:27 PM
NBrunk
Testing for Convergence of (Trigonometric) Series
Hello, and thanks in advance for the help.

I need to test for whether or not the following series converges:

Sum (from 1 to infinity) of sin(1/(n^2))

The only partial solution I can think of is that the max of the sine function is 1 and the minimum is 0 if you take the absolute value...but I'm not sure how to translate this into anything useful.

Thanks again guys...this forum is a great utility.
• Apr 8th 2010, 06:33 PM
tonio
Quote:

Originally Posted by NBrunk
Hello, and thanks in advance for the help.

I need to test for whether or not the following series converges:

Sum (from 1 to infinity) of sin(1/(n^2))

The only partial solution I can think of is that the max of the sine function is 1 and the minimum is 0 if you take the absolute value...but I'm not sure how to translate this into anything useful.

Thanks again guys...this forum is a great utility.

Hints: 1) the series is a positive one
2) For x > 0 close enough to zero, $\sin x < x$

Tonio
• Apr 8th 2010, 06:35 PM
dwsmith
Use the integral test.
• Apr 8th 2010, 06:43 PM
General
Use the limit comparison test with the convergent series $\sum_{n \geq 1} \frac{1}{n^2}$ ..