New posts in binomial-coefficients

A proof of the identity $ \sum_{k = 0}^{n} \frac{(-1)^{k} \binom{n}{k}}{x + k} = \frac{n!}{(x + 0) (x + 1) \cdots (x + n)} $.

combinatorics summation binomial-coefficients

Sum with binomial coefficients: $\sum_{m=1}^{k}\frac{1}{m^{2a}}\binom{k}{m}$ with constant a

combinatorics summation binomial-coefficients binomial-theorem

Combinatorial Analysis: Fermat's Combinatorial Identity

probability combinatorics binomial-coefficients

How prove this $\sum_{k=0}^n \binom{n}{k} \binom{(p-1)n}{k} \binom{pn+k}{k} = \binom{pn}{n}^2 $

binomial-coefficients

Combinatorial proof of $\binom{nk}{2}=k\binom{n}{2}+n^2\binom{k}{2}$

combinatorics discrete-mathematics binomial-coefficients combinatorial-proofs

Combinatoric formula summing one

probability combinatorics summation binomial-coefficients game-theory

Proving that $\sum_{k=0}^n\frac{1}{n\choose k}=\frac{n+1}{2^{n+1}}\sum_{k=1}^{n+1}\frac{2^k}{k}$

combinatorics summation binomial-coefficients fractions

How to efficiently calculate a row in pascal's triangle?

algorithm combinations binomial-coefficients pascals-triangle

How to show $\int_{\mathbb{R}}{t \choose x}^2{x \choose t}~dx = 1$

integration definite-integrals binomial-coefficients gamma-function

Infinite Series $\sum_{m=0}^\infty\sum_{n=0}^\infty\frac{m!\:n!}{(m+n+2)!}$

calculus real-analysis sequences-and-series binomial-coefficients closed-form

If $m,n\in N$ Prove that there is such a positive integer k, such that $(\sqrt{m}+\sqrt{m+1})^n=\sqrt{k}+\sqrt{k+1}$

number-theory elementary-number-theory binomial-coefficients problem-solving intuition

Vandermonde identity in a ring

abstract-algebra commutative-algebra polynomials ring-theory binomial-coefficients

Find $n$ and $k$ if $\:\binom{n\:}{k-1}=2002\:\:\:\binom{n\:}{k}=3003\:\:$

algebra-precalculus elementary-number-theory binomial-coefficients

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

sequences-and-series binomial-coefficients binomial-theorem

Computing $\sum_{n=1}^\infty\frac{2^{2n}H_{n+1}}{(n+1)^2{2n\choose n}}$

real-analysis integration sequences-and-series binomial-coefficients harmonic-numbers

Is there a closed form for the sum of the cubes of the binomial coefficients?

combinatorics binomial-coefficients closed-form

An interesting binomial summation

integration sequences-and-series summation binomial-coefficients

Lower bound on binomial coefficient

inequality binomial-coefficients information-theory

Proving the sum of squares of sine and cosine using the Cauchy product formula

power-series binomial-coefficients cauchy-product

Evaluate and prove by induction: $\sum k{n\choose k},\sum \frac{1}{k(k+1)}$ [duplicate]

discrete-mathematics summation induction binomial-coefficients