Proof by induction that alternating sum of binomial coefficients is $0$
7083
Alternating sum of binomial coefficients: given $n \in \mathbb N$, prove $\sum^n_{k=0}(-1)^k {n \choose k} = 0$
148442
Show that the sum $\sum_{k = 0}^n 2^k \binom{n}{k}$ is equal to $3^n$
33082
Proving $\sum_{i=0}^n 2^i=2^{n+1}-1$ by induction.
106183
Proof by Induction: Alternating Sum of Fibonacci Numbers
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
1258
Prove $3^n = \sum_{k=0}^n \binom {n} {k} 2^k$
153123
Proving by induction $4^n  0$
145048
Prove $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^n = n!$ and $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^m = 0$
158508
Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$
139426
Proving $ \binom n 0 ^2 + \binom n 1 ^2 + \dots + \binom n n ^2 = \binom { 2n} n $ without induction
136580
Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$
143337
How to prove that $\sum_{i=0}^n 2^i\binom{2n-i}{n} = 4^n$.
17638
Sum with binomial coefficients: $\sum_{k=0}^{n}{2n\choose 2k}$
49066
Give the combinatorial proof of the identity $\sum\limits_{i=0}^{n} \binom{k-1+i}{k-1} = \binom{n+k}{k}$
30338
How to prove that $\sum_{k=0}^n \binom nk k^2=2^{n-2}(n^2+n)$
44161
Using induction to prove $\sum_{k=0}^{N-1} 2^k = 2^N-1$