Proving $\sum_{k=1}^{n} k \binom{n}{k} = n \cdot 2^{n-1}$ by double counting
45204
Combinatorial proofs: having a difficult time understanding how to write them out
158508
Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$
10777
Proof of the identity $2^n = \sum\limits_{k=0}^n 2^{-k} \binom{n+k}{k}$
119759
Help ending a proof using binomial theorem: $\sum_{k=0}^n {n \choose k}\cdot\frac{(-1)^k}{k+1} = \frac{1}{n+1}$
112374
Evaluate $ \binom{n}{0}+\binom{n}{2}+\binom{n}{4}+\cdots+\binom{n}{2k}+\cdots$
113321
Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$
116356
Combinatorial proof of $2 \cdot 3^0 + 2 \cdot 3^1 + 2 \cdot 3^2 + \cdots 2 \cdot 3^{n-1} = 3^n-1$
141909
Prove ${2}^{n}\cdot(2m+1)-1 $ is invertible
114277
Proving in Discrete Structures Problem that $2^N = \binom{N}{0} + \binom{N}{1} + \binom{N}{2} + \dots + \binom{N}{N}$
89576
Proof of a binomial identity $\sum_{k=0}^n {n \choose k}^{\!2} = {2n \choose n}.$
1258
Prove $3^n = \sum_{k=0}^n \binom {n} {k} 2^k$
34299
Combinatorial proof of $\sum_{k=0}^n k \cdot k! = (n+1)! -1$
143365
Is $\sum_{i=1}^{n-1}i=\binom{n}{2}$?
64803
Counting two ways, $\sum \binom{n}{k} \binom{m}{n-k} = \binom{n+m}{n}$
18046
Prove the following equality: $\sum_{k=0}^n\binom {n-k }{k} = F_n$
4201
Prove $\sum\binom{n}{k}2^k = 3^n$ using the binomial theorem
145524
Proving this identity $\sum_k\frac{1}{k}\binom{2k-2}{k-1}\binom{2n-2k+1}{n-k}=\binom{2n}{n-1}$ using lattice paths