Use the binomial theorem to prove that for $n$ a positive integer the following holds
4327
proving $\left(1+\frac 1n\right)^{n} = 1 + \sum_{k=1}^n \{\frac 1{k!}\prod_{r=0}^{k-1}(1-\frac rn)\}$ using the binomial theorem
22154
Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n
91648
Binomial coefficient proof
111951
Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
125220
Solving binomial theorem via induction
20909
For each positive integer $n$, let $x_n=1/(n+1)+1/(n+2)+\cdots+1/(2n)$. Prove that the sequence $(x_n)$ converges.
79124
Proving $\binom {n-1}{r-1}=\sum_{k=0}^r(-1)^k\binom r k \binom{n+r-k-1}{r-k-1}$
52557
Derivation of binomial coefficient in binomial theorem.
45645
Using permutation or otherwise, prove that $\frac{(n^2)!}{(n!)^n}$ is an integer,where $n$ is a positive integer.
109576
Prove that $\binom{m+n}{m}=\sum\limits_{i=0}^m \binom{m}{i}\binom{n}{i}$
66019
Revisited: Binomial Theorem: An Inductive Proof
35956
Proof that a sum of Bernoulli rvs has Binomial distribution
16235
Prove by induction that every positive integer is represented by some binary number?
59638
How to prove this result on binomial coefficients?
75910
Combinatorial Proof of Combinatorial Identity involving $(-1)^k \binom {n-1}{k}$
81643
Proof that the hypergeometric distribution with large $N$ approaches the binomial distribution.