New posts in binomial-theorem

In which algebraic setting can I state (and prove) the binomial theorem?

abstract-algebra ring-theory binomial-theorem

Solving 9 sons puzzle

recreational-mathematics puzzle binomial-theorem

Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$

algebra-precalculus summation binomial-coefficients recreational-mathematics binomial-theorem

Newton's Binomial Theorem with $n<0$

binomial-theorem

Binomial theorem for $(1-x^2)^{n-\frac12}$

algebra-precalculus binomial-theorem

Why is $\sum\limits_{k=0}^{n}(-1)^k\binom{n}{k}^2=(-1)^{n/2}\binom{n}{n/2}$ if $n$ is even? [duplicate]

combinatorics summation binomial-coefficients binomial-theorem

Finding the Moment Generating function of a Binomial Distribution

statistics summation generating-functions binomial-theorem moment-generating-functions

Having trouble with proving this binomial identity. I have taken it as far as I can go.

combinatorics discrete-mathematics binomial-coefficients binomial-theorem

A Binomial Identity simplify

complex-analysis binomial-coefficients generating-functions binomial-theorem

Orthogonality for Binomial Coefficients

combinatorics summation binomial-coefficients binomial-theorem

Prove limit converges in definition of $e.$

exponential-function binomial-theorem limits-without-lhopital

Prove $\sum\binom{n}{k}2^k = 3^n$ using the binomial theorem

discrete-mathematics summation binomial-coefficients binomial-theorem

Show that $\sum\limits_{k=0}^n\binom{2n}{2k}^{\!2}-\sum\limits_{k=0}^{n-1}\binom{2n}{2k+1}^{\!2}=(-1)^n\binom{2n}{n}$

combinatorics summation binomial-coefficients binomial-theorem combinatorial-proofs

Proving $(1+\frac 1n)^{n} = 1 + \sum_{k=1}^n({\frac 1{k!}\prod_{r=0}^{k-1}(1-\frac rn))}$ using the binomial theorem

summation products binomial-theorem

Express $1 + \frac {1}{2} \binom{n}{1} + \frac {1}{3} \binom{n}{2} + \dotsb + \frac{1}{n + 1}\binom{n}{n}$ in a simplifed form

combinatorics binomial-coefficients binomial-theorem

Prove that there is no term independent of $x$ in the binomial expansion of $\left(x-\frac 1x\right)^{19}$

algebra-precalculus binomial-theorem

Finding the term independent of $x$ in $\left(e^x+e^{-x}+\ln e^{x+2}\right)^{20}$.

binomial-coefficients binomial-theorem