What is the sum of $\sum_{n=1}^{\infty} \frac{(-1)^{n+1}(2n+1)}{3^{n}}$
43903
Find the sum for $\sum_{n=1}^{\infty}(-1)^{(n+1)}\frac{2n+1}{3^n} $
78473
Showing $ \sum_{n=0}^{\infty} \frac{1}{(3n+1)(3n+2)}=\frac{\pi}{3\sqrt{3}}$
22636
Find the sum of the series $\sum \limits_{n=1}^{\infty} \frac{2^{-n}(n+3)}{(n+1)(n+2)}$
154544
Prove that $ \sum_{n=0}^\infty \frac{z^{2^n}}{1-z^{2^{n+1}}}=\frac{z}{1-z} $
104078
Calculate the sum of the infinite series $\sum_{n=0}^{\infty} \frac{n}{4^n}$
24373
Hint on computing the series $\sum_{n=2}^\infty \frac{1}{n^2-1}$.
104646
Question on simplification of $\sum_{n=1}^{\infty}\frac{2}{(2n+1)(2n+3)}$?
114280
Computing $\sum_{n=1}^∞\frac{1}{(n+1)(n+2)(n+3)....(n+p)}$
152227
How to sum this series to infinity: $\sum_{n=0}^{\infty} \frac1{2^{2^n}}$
89771
$\frac{1}{s-1}+\sum_{n=1}^{\infty}\left[\frac{1}{n^s}+\frac{1}{s-1}\left(\frac{1}{(n+1)^{s-1}} - \frac{1}{n^{s-1}}\right)\right]$
94943
Sum of series with addition: $\sum_{n=1}^\infty \frac{1}{n^2(n+1)}$
12812
Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots $
43320
Find the sum of the power series $\sum_{n=1}^\infty n*(n+1)*x^n$
94143
Evaluate:: $ 2 \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n+1}\left( 1 + \frac12 +\cdots + \frac 1n\right) $
64818
Use $\sum_{n=1}^\infty \frac{1}{n^4} = \frac{\pi^4}{90}$ to compute $\sum_{n=1}^\infty \frac{(-1)^n}{n^4}$
47706
Find the value of $ \sum_{n=1}^{\infty} \frac{n^3}{3^n} $
135927
Calculating $\sum_{n=1}^\infty\frac{1}{(n-1)!(n+1)}$