Proving Pascal's Identity algebraically, stuck with simplification
38206
Prove Pascal's Rule Algebraically
55481
Prove the identity $\binom{2n+1}{0} + \binom{2n+1}{1} + \cdots + \binom{2n+1}{n} = 4^n$
156564
Prove the identity $\sum_{{{\underset{k-even}{k=0}}}}^{n}{n \choose k}2^{k}=\frac{3^{n}+(-1)^{n}}{2}$
139426
Proving $ \binom n 0 ^2 + \binom n 1 ^2 + \dots + \binom n n ^2 = \binom { 2n} n $ without induction
122006
Proving combinatorial identity $\sum_{k=0}^{n}(-1)^k \binom{2n-k}k 2^{2n-2k} = 2n+1$ "directly"
7712
How to prove the both identity (matrix)
74887
Combinatorial proof of the identity ${n+1\choose k+1}={k\choose k}+{k+1\choose k}+...+{n-1\choose k}+{n\choose k}$
149249
Beginner: How to complete the induction case in a proof that all multiples are a product of the least common multiple
146810
How to derive this binomial identity?
133181
Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$
28936
Proving equation with binomial coefficient
33396
Generalizing a Trig Identity
47052
How can I simplify this expression involving binomial coefficients?
146053
Proving identities (mod $pq$) using Fermat's little theorem?
78359
Induction and Recursion Proof using Catalan Numbers
114411
Simple Proof of the Euler Identity $\exp{i\theta}=\cos{\theta}+i\sin{\theta}$
17491
Proof by Induction: Solving $1+3+5+\cdots+(2n-1)$