Prove $\binom{2n}{n}\geq\frac{4^n}{2n}$
54905
A classical inequality involving the central binomial coefficient
25004
Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically
64378
Proving a binomial sum identity $\sum _{k=0}^n \binom nk \frac{(-1)^k}{2k+1} = \frac{(2n)!!}{(2n+1)!!}$
157898
Showing that $\sum_{i=1}^n \frac{1}{i} \geq \log{n}$
4201
Prove $\sum\binom{n}{k}2^k = 3^n$ using the binomial theorem
24469
Prove $ 2<(1+\frac{1}{n})^{n}$
47072
Proving the inequality $\frac{9}4\ + \frac{3abc}4\ \ge ab+bc+ca$
117873
Combinatorially showing $\lim_{n\to \infty}{\frac{2n\choose n}{4^n}}=0$
66082
Using $\sqrt{1-t}\leq 1-\frac t2$ to show that $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots2n}\geq\frac1{2\sqrt n}$
136580
Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$
13525
Prove: If $n=2^k-1$, then $\binom{n}{i}$ is odd for $0\leq i\leq n$
5927
How to prove $a_1^m + a_2^m + \cdots + a_n^m \geq \frac{1}{a_1} + \frac{1}{a_2} + \cdots + \frac{1}{a_n}$
142589
Prove inequality of binomial theorem $\frac1{n^i}\binom{n}i \leq\frac1{m^i}\binom{m}i $.
46840
How to prove that $\sum_{r=0}^n\binom{n}{r}2^r=3^n$
58247
Prove $\sum_{k=0}^n \binom{n+k}{k}=\binom{2n+1}{n}$
76368
Proving the Binomial theorem
345
Proving $ \sum _{k=0} ^m \binom nk \binom{n-k}{m-k} = 2^m \binom {n}{m}$.