Evaluating $\sum_{n=1}^{\infty}\frac{(n-1)!}{(x+1)(x+2)(x+3)\cdots(x+n)}$ for positive real $x$
43509
Evaluating $\sum_{n=1}^{\infty}\frac{(n-1)!}{\prod_{r=1}^{n}(x+r)}$ for $x\in\mathbb{R}^{+}$
116723
Evaluating the sum $\sum_{n=1}^{\infty}\dfrac{(-1)^{n}}{n^{2}}$
7302
$\sum k! = 1! +2! +3! + \cdots + n!$ ,is there a generic formula for this?
124229
Simplify $\sum_{k=0}^{\infty} x^ky^{\frac{k(k+1)}{2}}$
107789
Sum of $\sum \limits_{n=0}^{\infty} \frac{1}{(kn)!}$
129801
Finding a closed form for $\sum^{n}_{k=1} \frac{k}{(k+1)!} $
141200
How do I check the series $\sum_{n=2}^{\infty} \frac{(-1)^n }{n+(-1)^n}$ for absolute convergence/conditional convergence?
127267
Evaluation of $\sum_{n=1}^{\infty}\frac{1}{n(2n+1)}=2-2\ln(2)$
30851
Find the summation $\frac{1}{1!}+\frac{1+2}{2!}+\frac{1+2+3}{3!}+ \cdots$
12480
Convergence of $\sum_{n=1}^{\infty} \frac{\frac{1}{2}+(-1)^n}{n}$
115420
Evaluate $\sum_{n=1}^{\infty} \frac{n}{n^4+n^2+1}$
101138
Convergent or divergent: $\sum_{k=1}^{\infty}\frac{2^{k}\cdot k!}{k^{k}}$
69084
What is the closed form for $\sum_{n=1}^\infty \frac1n - \frac1{n+1/p}$?
50972
Prove that $\sum_{x=1}^{n} \frac{1}{x (x+1)(x+2)} = \frac{1}{4} - \frac{1}{2 (n+1) (n+2)}$
913
Evaluating $\sum_{n=0}^{\infty}{\sin^{3}\left(3^{n}\right) \over 3^{n}}$
69978
Evaluating $\int_1^\infty \frac{1}{x(x^2+1)}\ dx$
63863
Evaluate: $\sum_{n=1}^{\infty}\frac{1}{n k^n}$