Calculating $\sum_{k=1}^\infty \frac{k^2}{2^k}=\frac{1}{2}+\frac{4}{4}+\frac{9}{8}+\frac{16}{16}+\frac{25}{32}+\cdots+\frac{k^2}{2^k}+\cdots$
27224
Infinite series $\sum_{k=1}^\infty \frac{k}{2^k}$ and $\sum_{k=1}^\infty \frac{k^2}{2^k}$
134610
Find the sum of finite series $S=\sum_{k=1}^{2015}{(-1)^{\frac{k(k+1)}{2}}}k$
70841
A simple series $\sum_{i=1}^\infty \frac{i}{2^i} = 2$
12812
Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots $
150148
Sum of $\sum^\infty_{n=2} \frac{1}{\ln{(n!)}}$
5054
Calculate $\sum\limits_{k=0}^{\infty}\frac{1}{{2k \choose k}}$
25395
Sum $\sum_{n=1}^\infty \frac{n^2}{(n+2)!}$
138313
How to sum $\sum_{n=1}^{\infty} \frac{1}{n^2 + a^2}$?
74120
Find the value of $\sum_{n=1}^{\infty} \frac{2}{n}-\frac{4}{2n+1}$
137027
Find the value of $\sum_{n=0}^\infty\frac{1}{9n^2+9n+2}$
78542
What is $\sum_{n=1}^{\infty} \frac{n}{2^{\sqrt{n}}}$?
92810
What is $\sum_{r=1}^\infty\frac{r+2}{2^{r+1}(r)(r+1)}$?
28378
Find the infinite sum of the series $\sum_{n=1}^\infty \frac{1}{n^2 +1}$
67752
Show that $\sum_{n = 1}^{+\infty} \frac{n}{2^n} = 2$
74117
Find the sum of series $\sum_{n=0}^{\infty}\frac{z^{kn}}{(kn)!}$
83641
The sum of the series $\frac{15}{16}+\frac{15}{16} \times \frac{21}{24}+\frac{15}{16} \times \frac{21}{24} \times \frac{27}{32}+\dots$
59253
Summing the power series $\sum\limits_{n=0}^\infty (-1)^n \frac{x^{2n+1}}{2n+1}\prod\limits_{k=1}^n\frac{2k-1}{2k} $