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## Homework Statement

[tex]\omega^2=(2/M)\sum_{n>0}\frac{A\sin(nk_0a)}{na}(1-\cos(nKa))[/tex]

A, a, and k_0 are constants, n is an integer.

I need to find [tex]\omega^2[/tex] and [tex]\frac{\partial\omega^2}{\partial K}[/tex], but I have no idea where to start.

## Homework Equations

Not sure, the stuff above.

## The Attempt at a Solution

I haven't done something like this in a while. I think I might be able to exploit

[tex] \sin A \cos B = \frac{1}{2} [ \sin(A-B)+\sin(A+B)][/tex]

but I'm still worried that the [tex]\frac{1}{n}[/tex] term is divergent...

Any ideas on where to start? I'm also considering a complex approach with Euler's formula, but I'm not sure how far I can go with this.

Many thanks!

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