Show that $P_n(X)=\frac{(X+i)^{2n+1} - (X - i)^{2n+1}}{2i}$ is of degree $2n$, even..., using the binomial coefficients formula
38871
How to obtain the complete factorization of $P_n(X)=\frac{(X+i)^{2n+1} - (X-i)^{2n+1}}{2i} = 0$
128913
A proof of $\sum_{i=1}^{n}(-1)^{i-1}\binom{n}{i}\frac{1}{i}=\frac{1}{1}+\frac{1}{2}+....+\frac{1}{n}$
28936
Proving equation with binomial coefficient
113321
Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$
151384
Summation of series involving binomial coefficients and polynomial of degree at most n-1
124131
Show that $(x-1)^2$ is a factor of $x^n -nx +n-1$
144814
If $p$ and $q$ are primes, which binomial coefficients $\binom{pq}{n}$ are divisible by $pq$?
17714
Proof $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k} = H_n$ by induction
30672
Show that $\sum\limits_{k=0}^n\binom{2n}{2k}^{\!2}-\sum\limits_{k=0}^{n-1}\binom{2n}{2k+1}^{\!2}=(-1)^n\binom{2n}{n}$
138683
Proving $\prod_{i=2}^{i=n} \left(1-\frac{1}{i^2}\right) = \frac{n+1}{2n}$ by induction
100361
Show that ord$_{p}2 = 2^{n + 1}$.
25054
Proving $\frac{1}{n+1} + \frac{1}{n+2}+\cdots+\frac{1}{2n} > \frac{13}{24}$ for $n>1,n\in\Bbb N$ by Induction
109576
Prove that $\binom{m+n}{m}=\sum\limits_{i=0}^m \binom{m}{i}\binom{n}{i}$
144571
A conjecture including binomial coefficients
68400
Proof that $\frac{(2n)!}{2^n}$ is integer
11612
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
42265
A proof that $\displaystyle\sum_{i=1}^{n}P''(r_i)/P'(r_i)=0$ for a degree $n$ polynomial