(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Does the follow serie converge:

[tex]\sum_{n=1}^\infty sin(\frac{1}{n^2})[/tex]

2. Relevant equations

For serie [tex]a_n[/tex] and [tex]b_n[/tex] if:

A = [tex]0 \leq a_n \leq b_n[/tex]

if [tex]b_n[/tex] converges then [tex]a_n[/tex] converges

3. The attempt at a solution

I think that I have to use the equation (see 2) and then with

B = [tex]\sum_{n=1}^\infty \frac{1}{n^2}[/tex]

I think that it is larger than A. However I need proof... Any suggestions.

Thanks in advance.

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# Homework Help: Convergence sum sin(1/n^2)

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