Evaluate $\sum_{n=0}^\infty (n+1)\left(\frac13\right)^n.$
6416
How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
33986
Calculate $\sum_{n=1}^{\infty}(\frac{1}{2n}-\frac{1}{n+1}+\frac{1}{2n+4})$
17438
Evaluate $\lim_{n\to \infty} \sum_{r=1}^n \frac {1}{2^r}\tan \left(\frac {1}{2^r}\right)$
98365
How to evaluate $\lim_{x \rightarrow \infty} \left(\left(\frac{x+1}{x-1}\right)^x -e^2\right){x}^2$
150563
Find the sum $\sum_{n=1}^{\infty} \frac{\ln n}{n(n- \ln n)}$
74120
Find the value of $\sum_{n=1}^{\infty} \frac{2}{n}-\frac{4}{2n+1}$
4253
How to calculate: $\sum_{n=1}^{\infty} n a^n$
125813
Convergence of $ \sum_{n=1}^\infty\left(\exp(\frac{(-1)^n}{n})-1\right)$?
14223
Find the infinite sum $\sum_{n=1}^{\infty}\frac{1}{2^n-1}$
92665
Find a function for the infinite sum $\sum_{n=0}^\infty \frac{n}{n+1}x^n$
84147
Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$
105186
Compute $\sum\limits_{n=0}^{\infty}\frac{{x^n}{z^n}}{n\beta + \alpha}$
56961
Evaluate the limit of $\sum_{n=1}^{\infty}\frac{n^2}{n!}$
141892
How to evaluate $\int_0^\infty \frac{1}{x^n+1} dx$
137027
Find the value of $\sum_{n=0}^\infty\frac{1}{9n^2+9n+2}$
19868
Evaluate: $ \sum _ {k=1}^{n}{\frac{k}{n}\binom{n}{k}t^k(1-t)^{n-k}}$
54661
How to find the sum $\sum\limits_{n=1}^{\infty}\frac{1}{n!(n^4+n^2+1)}$