Inequality involving factorial $\binom nk<(en/k)^k$
2708
Inequality ${n \choose k} \leq \left(\frac{en}{ k}\right)^k$
49783
A possible inequality related to binomial theorem (or, convex/concave functions)
41354
Binomial-coefficients if, k, m, n natural numbers and k \leq n the result of
35867
Squaring sides of an inequality
132732
Estimate of n factorial: $n^{\frac{n}{2}} \le n! \le \left(\frac{n+1}{2}\right)^{n}$
90904
Combinatorial proof of an identity with squared binomial coefficients
140857
Using Bernoulli's Inequality to prove an inequality
71797
Combinatorial argument for $\sum\limits_{k=i}^{n}\binom{n}{k}\binom{k}{i} = \binom{n}{i}2^{n-i}$
5332
Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$
148949
Find the value of $\sum_{k=1}^{n} k \binom {n} {k}$
87320
Proving identities like $\sum_{k=1}^nk{n\choose k}^2=n{2n-1\choose n}$ combinatorially
59638
How to prove this result on binomial coefficients?
133905
Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
23979
Inequality involving sides of a triangle
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
96945
General formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$.
136580
Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$