Binomial Theorem Derivative Identity
39724
Combinatorial Identities
128913
A proof of $\sum_{i=1}^{n}(-1)^{i-1}\binom{n}{i}\frac{1}{i}=\frac{1}{1}+\frac{1}{2}+....+\frac{1}{n}$
144571
A conjecture including binomial coefficients
107335
Prove equality between binomial coefficients.
11335
Proving Binomial Identity without calculus
25004
Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically
152084
Binomial-Theorem proof
92440
Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$
45725
Derivation of an identity with beta function.
155769
Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n-1}$ using the binomial theorem for $n\geq1$
137215
Cesaro identity for Fibonacci numbers: $ F_{2n} = \sum_{k=1}^n \binom{n}{k} F_k$
10777
Proof of the identity $2^n = \sum\limits_{k=0}^n 2^{-k} \binom{n+k}{k}$
4610
Proving an identity with a combinatorial proof: $\binom{n}{k}\binom{k}{r}=\binom{n}{r}\binom{n-r}{k-r}$
64328
How to prove that the Binet formula gives the terms of the Fibonacci Sequence?
96961
A proof for the identity $\sum_{n=r}^{\infty} {n \choose r}^{-1} = \frac{r}{r-1}$
65983
Combinatorial proof of binomial coefficient summation identity
76902
Variation on Vandermonde's identity