How to find the sum of $i(i+1)\cdots(i+k)$ for fixed $k$ between $i = 1$ and $n$?
110262
Finding a closed formula for $1\cdot2\cdot3\cdots k +\dots + n(n+1)(n+2)\cdots(k+n-1)$
113891
The limit of a sum of the form $a_0 \sqrt n + a_1 \sqrt {n + 1} +\cdots + a_k \sqrt {n + k}$
64581
How to find the sum $\sum\limits_{k=1}^n (k^2+k+1)k!$?
107071
Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n - 1}$ using the binomial theorem
63965
How can I compute the sum of $ {m\over\gcd(m,n)}$?
89367
Calculate $ S =\sum_{k=1}^n\frac {1}{k(k+1)(k+2)}. $
101017
What is the sum of $\sum\limits_{i=1}^{n}ip^i$?
57780
$\sum_{i=1}^n i\cdot i! = (n+1)!-1$ By Induction
114889
Solve summation $\sum_{i=1}^n \lfloor e\cdot i \rfloor $
34299
Combinatorial proof of $\sum_{k=0}^n k \cdot k! = (n+1)! -1$
48200
Simplify $\sum_{i=0}^n (i+1)\binom ni$
143365
Is $\sum_{i=1}^{n-1}i=\binom{n}{2}$?
151085
Simplify the sum $ \sum_{i=0}^{k}(-1)^i i \binom{n}{i} \binom{n}{k-i}$
148949
Find the value of $\sum_{k=1}^{n} k \binom {n} {k}$
119759
Help ending a proof using binomial theorem: $\sum_{k=0}^n {n \choose k}\cdot\frac{(-1)^k}{k+1} = \frac{1}{n+1}$
30851
Find the summation $\frac{1}{1!}+\frac{1+2}{2!}+\frac{1+2+3}{3!}+ \cdots$
51146
Sum of Infinite Series $1 + 1/2 + 1/4 + 1/16 + \cdots$