Proving $\binom{2n}{n} \geq \frac{2^{2n}}{n+1}$
88838
How can I prove this inequality for $n\geq 2$?
96945
General formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$.
34349
Prove that $\frac{1}{1+x_1}+\frac{1}{1+x_2}+\cdots+\frac{1}{1+x_n} \geq \frac{n}{\sqrt[n]{x_1x_2\cdots x_n}+1}$
73002
For $n \geq 2$, prove that $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})...(1- \frac{1}{n^2}) = \frac{n+1}{2n}$
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
73191
Proving that $\frac{1}{1\cdot 2} + \frac{1}{2\cdot 3} + \frac{1}{3 \cdot 4} +\ldots + \frac{1}{n(n+1)} = \frac{n}{n+1}$
155769
Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n-1}$ using the binomial theorem for $n\geq1$
32791
Proving this binomial identity $\sum_{k=0}^n {n+k \choose k} \frac{1}{2^{k}}= 2^{n}$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
113321
Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$
143337
How to prove that $\sum_{i=0}^n 2^i\binom{2n-i}{n} = 4^n$.
81842
How to prove by induction that $\frac{a^n+b^n}{2}\geq\left(\frac{a+b}{2}\right)^n$?
63510
Prove: $\binom{n}{k}^{-1}=(n+1)\int_{0}^{1}x^{k}(1-x)^{n-k}dx$ for $0 \leq k \leq n$
29828
Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$.
107258
Proving If $k \le \left\lfloor \frac{n}{2} \right\rfloor$ then $\binom{n}{k-1} < \binom{n}{k}$
109576
Prove that $\binom{m+n}{m}=\sum\limits_{i=0}^m \binom{m}{i}\binom{n}{i}$
121279
Proving an Combination formula $ \binom{n}{k} = \binom{n-1}{k}+\binom{n-1}{k-1}$