Combinatorial Proof of $\sum_{k=1}^{n-1} k\cdot k!= n!-1 $
36436
Proving $\sum_{k=1}^n k k!=(n+1)!-1$
118372
Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
133181
Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$
92704
Prove that $\sum_{k=1}^{n}k\binom{n}{k}=n\cdot2^{n-1}$
158508
Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
58247
Prove $\sum_{k=0}^n \binom{n+k}{k}=\binom{2n+1}{n}$
122006
Proving combinatorial identity $\sum_{k=0}^{n}(-1)^k \binom{2n-k}k 2^{2n-2k} = 2n+1$ "directly"
71564
Combinatorial proof of identity involving central binomial coefficients
107071
Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n - 1}$ using the binomial theorem
133905
Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
21000
Calculating $\sum_{k=1}^nk(k!)$ combinatorially
71797
Combinatorial argument for $\sum\limits_{k=i}^{n}\binom{n}{k}\binom{k}{i} = \binom{n}{i}2^{n-i}$
11612
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
110441
Closed form for a formula with a summation over $i\binom{n-i}{k-1}$, and combinatorial proof?
79652
Proof by induction that $2 + 4 + 6 + \cdots + 2n = n(n+1)$
17714
Proof $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k} = H_n$ by induction