# Thread: Testing for Convergence of (Trigonometric) Series

1. ## 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.

2. 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

3. Use the integral test.

4. Use the limit comparison test with the convergent series $\sum_{n \geq 1} \frac{1}{n^2}$ ..

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# convergence of series with trigonometric functions

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