Proving $T(n) = 1 + \sum_{j=0}^{n-1} T(j)$, $T(0)=1$ implies $T(n)=2^n$
105882
Prove that the sequence with $T(0)=1$ and $T(n) = 1 + \sum_{j=0}^{n-1}T(j)$ is given by $T(n)=2^n$
55266
Prove that $(n+1)^{n-1}<n^n$
120976
Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $
58428
Proving $\sum_{k=0}^{n} {k \choose a} {n-k \choose b} = {n+1\choose a+b+1}$
128913
A proof of $\sum_{i=1}^{n}(-1)^{i-1}\binom{n}{i}\frac{1}{i}=\frac{1}{1}+\frac{1}{2}+....+\frac{1}{n}$
92784
Intuitive (combinatorial) proof of $2^n=\sum_{k=0}^n {n\choose k}$
1258
Prove $3^n = \sum_{k=0}^n \binom {n} {k} 2^k$
36436
Proving $\sum_{k=1}^n k k!=(n+1)!-1$
151553
Big-O proof showing that t(n) is O(1)
33082
Proving $\sum_{i=0}^n 2^i=2^{n+1}-1$ by induction.
113321
Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$
65672
Proof of the summation $n!=\sum_{k=0}^n \binom{n}{k}(n-k+1)^n(-1)^k$?
55428
Inductive proof of $a_n = 3*2^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2*a_{n-2}, a_1 = 1, a_2 = 8$
69131
Different proofs of $\,a^n-b^n =(a-b)\sum_{i=0}^{n-1} a^i b^{n-1-i} $?
145048
Prove $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^n = n!$ and $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^m = 0$
17714
Proof $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k} = H_n$ by induction
8360
$\sum_i x_i^n = 0$ for all $n$ implies $x_i = 0$