# Tagged Questions

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### Calculate ch(0.2) to the nearest 0.01

Help me calculate ch(0.2) to the nearest 0.01. I tried to rewrite ch as a series but I still don't know how to evaluate it and what to do with factorial Help me please. it's very important
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### How to find the value of this sum?

The sum below numerically (to 13th digit at least) is the same as $\ln 2$. So there should be a way to prove it analytically, but I haven't succeeded. Any suggestions? ...
$S_n=\sum_{i=1}^n\big\{ \cosh\big(\frac{1}{\sqrt{n+i}}\!\big) -n\big\}$ as $n\to\infty$ I stumbled on this question as an reading about Riemannian sums as in $$\int_a^b f(x)\,dx =\lim_{x\to ... 1answer 94 views ### How to simplify this equation? How to simplify this equation? I know that: \sin^2 p+\cos^2 p = 1 But how to go further? 2answers 133 views ### Evaluating a sum with \cosh In my integration adventures, I ran into this sum:$$\sum_{n=1}^{\infty}\frac{1}{\cosh(\pi an)(4n^{2}-1)}$$I know that \sum_{n=1}^\infty \frac{1}{\cosh(\pi n)} has a nice closed form, so I was ... 2answers 308 views ### Series \sum\limits_{n=1}^\infty \frac{1}{\cosh(\pi n)}= \frac{1}{2} \left(\frac{\sqrt{\pi}}{\Gamma^2 \left( \frac{3}{4}\right)}-1\right) I was playing around with Mathematica and found that$$\sum_{n=1}^\infty\frac1{\cosh(\pi n)} = \frac12\left(\frac{\sqrt{\pi}}{\Gamma \left(\tfrac34\right)^2}-1\right)$$Does anybody know how to ... 3answers 399 views ### Show \sum_{n=1}^{\infty}\frac{\sinh\pi}{\cosh(2n\pi)-\cosh\pi}=\frac1{\text{e}^{\pi}-1} and another Show that :$$\sum_{n=1}^{\infty}\frac{\cosh(2nx)}{\cosh(4nx)-\cosh(2x)}=\frac1{4\sinh^2(x)}\sum_{n=1}^{\infty}\frac{\sinh\pi}{\cosh(2n\pi)-\cosh\pi}=\frac1{\text{e}^{\pi}-1}
For $\displaystyle\int_0^{\infty}x^n\frac{\sinh ax}{\cosh bx}\text{d}x$, $\left|a\right|<b$ I think we can evaluate \$\displaystyle\int_{0}^{\infty }{{{\text{e}}^{cx}}\frac{\sinh ax}{\cosh ...