New posts in Binomial Theorem

Continuous version of binomial expansion

How many ways can I go from 1 to 10 in the following diagram?

Evaluating $\int\limits_a^b x (b-x)^{n-1} (x-a)^{k-n} dx$

Proving that $\sum_{k=0}^{2n} {2k \choose k } {2n \choose k}\left( \frac{-1}{2} \right)^k=4^{-n}~{2n \choose n}.$

Root of unity filter

Help on proof of $\binom{n}{0}^2 + \binom{n}{1}^2 + ... + \binom{n}{n}^2 = \binom{2n}{n}$

Question related to Pascal Triangles and Counting Patterns

How can I prove $\frac {d}{dx} {x^n} = n x^{n-1}$ for $ n \in \Bbb R$ without circular reasoning?

Remainder on division with $22$

Proving $\sum\limits_{k=0}^{\infty}\binom {m-r+s}k\binom {n+r-s}{n-k}\binom {r+k}{m+n}=\binom rm\binom sn$