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Find the convergent sum and find the sum of first five terms

[tex]

\sum_{n=1}^{\infty} \frac{sin(nx)}{2^nn}

[/tex] from 1 to infinity.

I have found so far that:

[tex]

\sum_{n=1}^{\infty} \frac{sin(nx)}{2^n} = \frac{2sin(x)}{5-4cos(x)}

[/tex] I am not sure how to consider the [tex]\frac{1}{n}[/tex] term.

Can someone please help?

[tex]

\sum_{n=1}^{\infty} \frac{sin(nx)}{2^nn}

[/tex] from 1 to infinity.

I have found so far that:

[tex]

\sum_{n=1}^{\infty} \frac{sin(nx)}{2^n} = \frac{2sin(x)}{5-4cos(x)}

[/tex] I am not sure how to consider the [tex]\frac{1}{n}[/tex] term.

Can someone please help?

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