New posts in Binomial Theorem

Proving Riordan's identity that $\sum_{k=1}^{n} {n-1 \choose k-1} \frac{k!}{n^k}=1$

In the ring $\mathbb{Z}_p$, $p$ is prime, $(a+b)^p=a^p+b^p$ proof?

summing this binomial series

Why do binomial expansions involving surds get closer to integers as they get larger?

Proving $\int_{0}^{1} \frac{\tanh^{-1}\sqrt{x(1-x)}}{\sqrt{x(1-x)}}dx=\frac{1}{3}(8C-\pi\ln(2+\sqrt{3}))$ for an identity of Srinivasa Ramanujan

Proving a sum of a strange series $ \sum_{i=1}^{n} 11i^{10}-55i^9+165i^8-330i^7+462i^6 -462i^5+330i^4-165i^3+55i^2-11i+1 = n^{11} $

Proving that $ \sum_{k=0}^\infty\frac1{2k+1}{2k \choose k}^{-1}=\frac {2\pi}{3\sqrt{3}} $

For what value of $m$ the is sum $\sum_{i = 0}^{m} {10 \choose i}{20 \choose m - i}$ where ${p\choose q} = 0$, if $p<q$, a maximum

Simplification of $\displaystyle{0 \binom{n}{0} + 2 \binom{n}{2} + 4 \binom{n}{4} + 6 \binom{n}{6} + \cdots}$

Factorise $x^4+y^4+(x+y)^4$