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

Is this series convergent for all real x:

[tex]\sum[/tex][tex]^{\infty}_{k=2}[/tex][tex]\frac{sin(kx)}{ln(k)}[/tex]

2. Relevant equations

3. The attempt at a solution

This series is less than

[tex]\frac{1}{ln(2)}[/tex][tex]\sum[/tex][tex]^{\infty}_{k=2}[/tex]sin(kx)

which is less than [tex]\frac{\pi}{x ln2}[/tex]. So, the series is bounded for all x. I'm thinking that the Dirichlet Test would show that this series converges.

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# Homework Help: Convergent Series

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