why $\sum_{h=0}^{\infty}{\dfrac{h}{2^h}} = 2$
37771
Sum of a power series $n x^n$
44970
Show $\sum_{n=0}^\infty\frac{1}{a^2+n^2}=\frac{1+a\pi\coth a\pi}{2a^2}$
128285
Why is $ \sum_{n=0}^{\infty}\frac{x^n}{n!} = e^x$?
100866
Why is $\int_{0}^{\infty} \frac {\ln x}{1+x^2} \mathrm{d}x =0$?
32042
Convergence of $\sum_{n=1}^\infty \frac{n^2}{2^n}$
24022
Compute $\int _0 ^{2\pi} (\sum_{n=1}^\infty \frac {\cos(nx)}{2^n})^2 dx$
326
Find $\sum_{k=1}^{\infty}\frac{1}{2^{k+1}-1}$
104078
Calculate the sum of the infinite series $\sum_{n=0}^{\infty} \frac{n}{4^n}$
3356
Why $\sum_{k=0}^m x^k $ is equal to $\dfrac{x^{m+1}-1}{x-1} $?
104753
$\sum_{k=1}^nH_k = (n+1)H_n-n$. Why?
103572
Does $\sum_{m=1}^{\infty}\sum_{n=1}^{\infty}a_{mn}^3=\sum_{n=1}^{\infty}\sum_{m=1}^{\infty}a_{mn}^3$ occur here?
152227
How to sum this series to infinity: $\sum_{n=0}^{\infty} \frac1{2^{2^n}}$
72377
Show that $\sum_{n=1}^\infty r^n\cos(n\theta)=\dfrac{r\cos\theta -r^2}{1-2r\cos\theta+r^2}$ whenever $0<r<1$.
144078
What does $\sum_{k=0}^\infty \frac{k}{2^k}$ converge to?
64223
Infinite Series $\sum\limits_{n=1}^\infty\left(\frac{H_n}n\right)^2$
2678
Values of $\sum_{n=0}^\infty x^n$ and $\sum_{n=0}^N x^n$
61850
Compute $\sum_{k=0}^{\infty}\frac{1}{2^{k!}}$