Does a general formula for $\sum_{r=1}^{n}r^k$ proof exist?
45084
How is Faulhaber's formula derived?
44328
Prove that $\sum_{k=1} ^ n k^{-1} = \ln(n) + O(1)$
3798
Finding formula for sum $S_n = \sum_{i=1}^n i(i-1)$
1167
How to prove that $\sum_{k=0}^{n}(-1)^k \binom {n}{k}=0 $
108318
counting proof for $\sum_{k=0}^{n-1} 2^{k} = 2^n - 1$
50226
Prove the identity $\sum_{k=0}^{n}\sum_{r=0}^{k} \binom{k}{r} \binom{n}{k} = 3^n$
1158
How to prove this binomial identity $\sum_{r=0}^n {r {n \choose r}} = n2^{n-1}$?
99453
Sum of $k$-th powers
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
18046
Prove the following equality: $\sum_{k=0}^n\binom {n-k }{k} = F_n$
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
34299
Combinatorial proof of $\sum_{k=0}^n k \cdot k! = (n+1)! -1$
86348
Proving $\sum\limits_{k=0}^{n-1} \Bigl[x + \frac{k}{n}\Bigr] = [nx]$
20317
Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$
96945
General formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$.
119107
Is it true that $\sum_{k=3}^{n}\binom{n}{k}\binom{k}{3} = \binom{n}{3}\binom{n-3}{k-3}$?