Prove $ \sum \frac{\cos(n)} { \sqrt n}$ is bounded.
How can I prove $\sum \cos(n)$ is bounded. Can It be done using $\cos$ as real part of complex number as I showed in question ?
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Yes your approach is right. I believe you want to prove the convergence of the series using Dirichlet test. – science Apr 17 '15 at 00:29
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Are you trying to show $\sum \frac {\cos n}{\sqrt n}$ converges? – zhw. Apr 17 '15 at 00:31
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yes i am but using abels theorem – user230463 Apr 17 '15 at 00:34
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Fine, but you stated a different problem. I will edit now. – zhw. Apr 17 '15 at 01:06