Convergence of a trigonometric series

Real Analysis
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Riemann
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Joined: Sat Nov 14, 2015 6:32 am
Location: Melbourne, Australia

Convergence of a trigonometric series

#1

Post by Riemann »

Prove that the series

$$\sum_{n=1}^{\infty} \sin \left[\pi \left( 2+\sqrt{3} \right)^n \right]$$

converges.
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$
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