New posts in binomial-theorem

If $n\ge2$, Prove $\binom{2n}{3}$ is even.

elementary-number-theory discrete-mathematics combinations binomial-theorem

Rings in which binomial theorem holds for at least one integer $n>2$

reference-request ring-theory binomial-theorem

Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$ [duplicate]

combinatorics summation binomial-theorem

Root of unity filter

combinatorics complex-numbers summation binomial-theorem roots-of-unity

Binomial theorem for non integers ? O_o ??

binomial-theorem

Arc Length Integral of $x^x$ from 0 to 1 in closed form.

calculus summation exponentiation binomial-theorem arc-length

Prove the identity $\binom{2n+1}{0} + \binom{2n+1}{1} + \cdots + \binom{2n+1}{n} = 4^n$

summation binomial-coefficients binomial-theorem

Combinatorial identity from squaring the binomial expansion

combinatorics binomial-coefficients binomial-theorem combinatorial-proofs

Show that $\sum_{k=1}^n \binom{n}{k}k^2=n^2\cdot \:2^{n-2}+n\cdot \:2^{n-2}$.

combinatorics generating-functions binomial-theorem

find the formula of trinomial expansion

binomial-theorem multinomial-coefficients

Binomial expansion of $(1-x)^n$

binomial-theorem

Is it true that $\lim_{m\to\infty} \sum_{k=0}^{\frac{m-1}{2}} {m\choose{k}}(a^{k+1}(1-a)^{m-k}+a^k(1-a)^{m-k+1})=\min(a,1-a)$?

limits binomial-coefficients binomial-theorem

Ways to find $\frac{1}{2\cdot4}+\frac{1\cdot3}{2\cdot4\cdot6}+\frac{1\cdot3\cdot5}{2\cdot4\cdot6\cdot8}+\cdots$

sequences-and-series factorial binomial-theorem

Simplify the expression $\binom{n}{0}+\binom{n+1}{1}+\binom{n+2}{2}+\cdots +\binom{n+k}{k}$ [duplicate]

algebra-precalculus binomial-coefficients binomial-theorem

When is $(a+b)^n \equiv a^n+b^n$?

algebra-precalculus finite-fields equivalence-relations binomial-theorem

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

discrete-mathematics binomial-theorem

How to show $\lceil ( \sqrt3 +1)^{2n}\rceil$ where $n \in \mathbb{ N}$ is divisible by $2^{n+1}$

binomial-theorem

How to show that $ \left(1+\frac{1}{n} \right)^n = \sum_{i=0}^{n}\frac{1}{i!}\left(\prod_{j=0}^{i-1}\left(1 - \frac{j}{n}\right)\right)$ [duplicate]

summation products binomial-theorem

Poisson random variables and Binomial Theorem

probability probability-theory probability-distributions statistical-inference binomial-theorem

Let $S$ be the sum of all the real coefficients of the expansion of $(1+ix)^{2020}$. What is $\log_{2}|S|$?

complex-numbers logarithms binomial-theorem