New posts in Binomial Theorem

Pairs of non-empty disjoint sets

Evaluate $\sum_{k=1}^n\frac{1}{k}\binom{n}{k}$

Show that $e^{1-n} \leq \frac {n!}{n^n}$

Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n-1}$ using the binomial theorem for $n\geq1$

Prove that $7^{100} - 3^{100}$ is divisible by $1000$

Coefficient of $x^{n-2}$ in $(x-1)(x-2)(x-3)\dotsm(x-n)$

Expansion of Binomial Coefficient $(1+x+x^2)^n$

About the identity $\sum\limits_{i=0}^{\infty}\binom{2i+j}{i}z^i=\frac{B_2(z)^j}{\sqrt{1-4z}}$

Is this sum $\sum_{k=0}^{n}{n\choose k}\sum_{i=0}^{k}(-1)^i{k\choose i}H_{n+k-i}=H_{2n}$ correct?

How to evaluate $\binom{2}{2}\binom{10}{3} + \binom{3}{2}\binom{9}{3} + \binom{4}{2}\binom{8}{3} + \ldots + \binom{9}{2}\binom{3}{3}$