The closed form for $\sum_{n\geq1}\frac1{n(n+1)(n+2)\cdots(n+m)}$
42216
Sum of infinite series $\sum_{i=1}^{\infty} \frac 1 {i(i+1)(i+2)...(i+n)}$
42736
Is there a closed form for $\sum_{k=0}^n \frac{x^k}{k!}$?
37007
Evaluating $\sum_{k=1}^{n} \frac{1}{k(k+1)}$
35342
Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
119759
Help ending a proof using binomial theorem: $\sum_{k=0}^n {n \choose k}\cdot\frac{(-1)^k}{k+1} = \frac{1}{n+1}$
133181
Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$
133070
Finding a closed form expression for the recurrence relation $a(n,k+1)=(k+1)^n+\sum_{m=1}^k {k+1\choose m}a(n,m)$
29170
Find the sum of the series $\sum \frac{1}{n(n+1)(n+2)}$
40784
$\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n>m\geq 0$
36742
The sum of $(-1)^n \frac{\ln n}{n}$
113891
The limit of a sum of the form $a_0 \sqrt n + a_1 \sqrt {n + 1} +\cdots + a_k \sqrt {n + k}$
119606
Closed form of summation
107179
Partial fraction expansion of $\frac{1}{x(x+1)(x+2)\cdots(x+n)}$
114280
Computing $\sum_{n=1}^∞\frac{1}{(n+1)(n+2)(n+3)....(n+p)}$
112929
How do I prove $\frac 34\geq \frac{1}{n+1}+\frac {1}{n+2}+\frac{1}{n+3}+\cdots+\frac{1}{n+n}$
98941
Closed formula for the sums $\sum\limits_{1 \le i_1 < i_2 < \dots < i_k \le n} i_1 i_2 \cdots i_k $?
34299
Combinatorial proof of $\sum_{k=0}^n k \cdot k! = (n+1)! -1$