New posts in Binomial Theorem

Find $r$ which maximizes $\binom{20}r\binom{20}0+\binom{20}{r-1}\binom{20}1+\binom{20}{r-2}\binom{20}2+\cdots+\binom{20}0\binom{20}r$

Show that $(n+1)^{2/3} -n^{2/3} <\frac{2}{3} n^{-1/3}$ for all positive integers

A closed form for $\sum_{k=0}^n \frac{ (-1)^k {n \choose k}^2}{k+1}$

Finding remainder when $5^{99}$ is divided by $13$

Proving that $\int_{0}^{1}x^{n-1}(1-x)^n \mathrm dx =\frac{1}{n {2n\choose n}}$

Struggle with binomial coefficient notations

An interesting problem of polynomials

Show that $\sum_{k=0}^{n+1}\left(\binom{n}{k}-\binom{n}{k-1}\right)^2 = \frac{2}{n+1}\binom{2n}{n}$

Prove $\forall n\ge0,43\mid 6^{n+2}+7^{2n+1}$ in three ways

Expression of $x^n+\frac1{x^n}$ by $x+\frac1{x}$ where $n$ is a positive odd number.