Compute $\sum\limits_{n=0}^{\infty}\frac{1}{(2n+1) . 4^n} $
13085
Evaluate $ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots$
123955
How to compute $\sum\limits_{k=0}^n (-1)^k{2n-k\choose k}$?
125148
Summation of series $\sum_{k=0}^\infty 2^k/\binom{2k+1}{k}$
4638
What is the value of $\lim_{n\to \infty} \sum_{j=n}^{4n} {4n \choose j}\bigl(\frac{1}{4}\bigr)^{j} \bigl(\frac{3}{4}\bigr)^{4n-j}$?
104078
Calculate the sum of the infinite series $\sum_{n=0}^{\infty} \frac{n}{4^n}$
19899
infinite series of the form $\sum\limits_{k=1}^{\infty}\frac{1}{a^{k}+1}$
2877
Show $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$
115420
Evaluate $\sum_{n=1}^{\infty} \frac{n}{n^4+n^2+1}$
89263
Find the limit $\lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k+n}$
107789
Sum of $\sum \limits_{n=0}^{\infty} \frac{1}{(kn)!}$
6416
How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
43903
Find the sum for $\sum_{n=1}^{\infty}(-1)^{(n+1)}\frac{2n+1}{3^n} $
30895
Compute the sum of the series $\sum_{n=1}^{\infty} \frac{1}{n \cdot 2^n}$
102531
Prove $\sum\limits^m_{k=0} \frac{2n-k\choose k}{2n-k\choose n}\frac{2n-4k+1}{2n-2k+1}2^{n-2k}=\frac{n\choose m}{2n-2m\choose n-m}2^{n-2m}$ for-
89698
Please help with $\sum\limits_{r=1}^{N}\frac{2r+3}{3^r(r+1)}$
5974
Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$
109059
Evaluate $\lim\limits_{n\to \infty}\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{6n}$