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Continuous on the previous question, can we get a closed form for these? $$\begin{align} & \sum\limits_{n=1}^{\infty }{\frac{n+3}{{{n}^{3}}+\ln n}} \\ & \sum\limits_{n=1}^{\infty }{\left( 1-\cos \frac{\pi }{n} \right)} \\ \end{align}$$ I think the first one has no closed form, but maybe the second one does?

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If you're continuing a prior question, it is recommended to link to the prior question. –  anorton Feb 5 '13 at 3:01
@anorton : The previous one is just about the convergency test –  Ryan Feb 5 '13 at 3:05
For those who don't remember all of Ryan's questions, here's the aforementioned question: math.stackexchange.com/questions/294461/two-simple-series –  anorton Feb 5 '13 at 3:10
Mathematica doesn't know closed forms for either, and their numerical values don't turn up anything in the Inverse Symbolic Calculator. –  Antonio Vargas Feb 5 '13 at 3:19

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