Calculate the sum $\sum_{k=0}^{\infty} a^{\frac{k(k-1)}{2}}r^k$
124229
Simplify $\sum_{k=0}^{\infty} x^ky^{\frac{k(k+1)}{2}}$
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} $
108010
Evaluating $\sum_{k=1}^{\infty}\left(\frac{\sin(tk)}{k}\right)^2$
17686
Evaluate the infinite series $\sum_{r=1}^{\infty} \frac{2^{-r}}{r^{2}}$
17713
What's the value of $\sum\limits_{k=1}^{\infty}\frac{k^2}{k!}$?
27224
Infinite series $\sum_{k=1}^\infty \frac{k}{2^k}$ and $\sum_{k=1}^\infty \frac{k^2}{2^k}$
50812
Partial sum of the series $\sum\limits_{r=1}^{\infty} \frac{1}{r(r+1)}$
125915
An Infinite Double Summation $\sum_{k=1}^{\infty} \sum_{n=1}^{\infty} \frac{1}{n^2k^2(n+k)^2}$?
76387
Evaluate the series $\sum_{n=1}^{\infty} \frac{2^{[\sqrt{n}]}+2^{-[\sqrt{n}]}}{2^n}$
145154
Calculating limit of $\sum_{k = 0}^\infty \frac{n^k}{k!} \vert k - n \vert$
17056
How to find answer to the sum of series $\sum_{n=1}^{\infty}\frac{n}{2^n} $
142985
Finding sum of series $\sum^{\infty}_{k=0}\frac{(k+1)(k+2)}{2^k}$
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 $
43509
Evaluating $\sum_{n=1}^{\infty}\frac{(n-1)!}{\prod_{r=1}^{n}(x+r)}$ for $x\in\mathbb{R}^{+}$
144078
What does $\sum_{k=0}^\infty \frac{k}{2^k}$ converge to?