Use binomial expansion to show the following inequality
123523
Showing $\left(1+\frac{1}{n}\right)^n$ is an increasing sequence by comparing the binomial expansions term by term
4855
How to show that this binomial sum satisfies the Fibonacci relation?
77026
Proof with inequalities
30672
Show that $\sum\limits_{k=0}^n\binom{2n}{2k}^{\!2}-\sum\limits_{k=0}^{n-1}\binom{2n}{2k+1}^{\!2}=(-1)^n\binom{2n}{n}$
135550
Inequality question­
88838
How can I prove this inequality for $n\geq 2$?
86209
Show this inequality $\frac{n}{a_1 - a_0} + \frac{n - 1}{a_2 - a_1} + \cdots + \frac{1}{a_n - a_{n-1}} \ge \sum_{k=1}^n \frac{k^2}{a_k}$
70926
Showing that for $n\geq 3$ the inequality $(n+1)^n<n^{(n+1)}$ holds
128856
Show the result of the following infinite sum, based on a binomial random variable conditioned on a Poisson random variable
104125
How prove this inequality??
40784
$\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n>m\geq 0$
90293
How expand Binomial[n, k] for k >= 6?
15232
Proving an inequality involving real powers
22962
How to show $\binom{2p}{p} \equiv 2\pmod p$?
54905
A classical inequality involving the central binomial coefficient
59905
Proving the inequality $\frac{n^k}{k^k}\leq\binom{n}{k}\leq\frac{n^k}{k!}$ involving binomial coefficient.
148442
Show that the sum $\sum_{k = 0}^n 2^k \binom{n}{k}$ is equal to $3^n$