limit of a sum: $\sum_{n} = 1+x+2x^2+3x^3+...+nx^n$
6416
How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
54661
How to find the sum $\sum\limits_{n=1}^{\infty}\frac{1}{n!(n^4+n^2+1)}$
37260
Calculate $\lim_{n\to{+}\infty}{(\sqrt{n^{2}+n}-n)}$
80177
Sum from $n=1$ to $N$ of $\sin(nx)/2^n$
89263
Find the limit $\lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k+n}$
132264
Is there a (basic) way to understand why a limit cannot be brought inside of a sum, in certain situations?
17375
When is the limit of a sum equal to the sum of limits?
125087
Evaluate the limit of ratio of sums of sines (without L'Hopital): $\lim_{x\to0} \frac{\sin x+\sin3x+\sin5x}{\sin2x+\sin4x+\sin6x}$
101351
Calculate $\int \limits {x^n \over 1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+...+\frac{x^n}{n!}} dx$ where $n$ is a positive integer.
113891
The limit of a sum of the form $a_0 \sqrt n + a_1 \sqrt {n + 1} +\cdots + a_k \sqrt {n + k}$
137155
Sum $ \sum\limits_{k=1}^{\infty} \frac{k^2}{2^k}$
43903
Find the sum for $\sum_{n=1}^{\infty}(-1)^{(n+1)}\frac{2n+1}{3^n} $
25395
Sum $\sum_{n=1}^\infty \frac{n^2}{(n+2)!}$
71798
$\lim_{n\to \infty}\frac{1}{n} \sum_{k=1}^n x_k =x\;$ given $\;\lim_{n\to \infty} x_n= x\;?$
22636
Find the sum of the series $\sum \limits_{n=1}^{\infty} \frac{2^{-n}(n+3)}{(n+1)(n+2)}$
56961
Evaluate the limit of $\sum_{n=1}^{\infty}\frac{n^2}{n!}$
5436
How to prove $\lim \limits_{x \to 1^-} \sum\limits_{n=0}^\infty (-1)^nx^{n²} = \frac{1}{2} \ $?