# Math Help - Test the following series for convergence..

1. ## Test the following series for convergence..

$\sum_{n=1}^{\infty} \dfrac{1}{n^{sinh(n)}}$

2. Because is $\sinh 1 = 1.1752011936438...$ and the function $\sinh (*)$ is [strongly] increasing, for all n will be...

$\frac{1}{n^{\sinh n}} < \frac{1}{n^{1.1}}$ (1)

Now the series...

$\sum_{n=1}^{\infty}\frac{1}{n^{1.1}}$ (2)

... converges so that...

Kind regards

$\chi$ $\sigma$