Formula for the sum of $\ n\cdot 1 + (n-1)\cdot 2 + ... + 2 \cdot (n-1) + 1\cdot n$
11612
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
158004
A formula for $1^4+2^4+...+n^4$
74294
How to simplify $\sum_{i=1}^{k}\binom{n + i - 1}{i}$?
60860
Combinatorial proof of $\sum_{i = 0}^{n} \binom{i}{r - 1} = \binom{n + 1}{r}$ and then use result to find a formula for $1^2 + 2^2 + \ldots + n^2$
145048
Prove $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^n = n!$ and $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^m = 0$
51146
Sum of Infinite Series $1 + 1/2 + 1/4 + 1/16 + \cdots$
60902
Find general solution for the equation $1 + 2 + \cdots + (n − 1) = (n + 1) + (n + 2) + \cdots + (n + r) $
112374
Evaluate $ \binom{n}{0}+\binom{n}{2}+\binom{n}{4}+\cdots+\binom{n}{2k}+\cdots$
6539
Prove $\sum_{i=1}^n i! \cdot i = (n+1)! - 1$?
99003
How do we calculate this sum $\sum_{n=1}^{\infty} \frac{1}{n(n+1)\cdots(n+p)}$?
138172
Find the sum to n terms of the series $\frac{1}{1.2.3}+\frac{3}{2.3.4}+\frac{5}{3.4.5}+\frac{7}{4.5.6}+\cdots$..
112036
sum of series $\frac{n}{1\cdot 2 \cdot 3}+\frac{n-1}{2\cdot 3\cdot 4}+\frac{n-2}{3\cdot 4 \cdot 5}+\cdots \cdots n$ terms
91933
Evaluate $\sum_{k=1}^nk\cdot k!$
91458
Sum of the series $\binom{n}{0}-\binom{n-1}{1}+\binom{n-2}{2}-\binom{n-3}{3}+..........$
30851
Find the summation $\frac{1}{1!}+\frac{1+2}{2!}+\frac{1+2+3}{3!}+ \cdots$
3798
Finding formula for sum $S_n = \sum_{i=1}^n i(i-1)$
98933
Calculating the sum of $f(x) = \sum_{n=0}^{\infty} {n \cdot 2^n \cdot x^n}$