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Convergence of series with modified denominator Clever derivation of $\arcsin(x)$ Taylor series http://trungtuan.files.wordpress.com/2009/06/monthly_mai_2008.pdf http://www.mat.uniroma2.it/~perfetti/lavori/problemi%20pubblicati/problemipubblicati.html Does the series $ \sum\limits_{n=1}^{\infty} \frac{1}{n^{1 + |\sin(n)|}} $ converge or diverge?