New posts in binomial-coefficients

Negative Binomial Coefficients

combinatorics binomial-coefficients

Sum of product of binomial coefficient

binomial-coefficients

How should I solve combination addition like this?

combinatorics summation combinations binomial-coefficients combinatorial-proofs

partial sum involving factorials

sequences-and-series binomial-coefficients

Category of binomial rings

commutative-algebra category-theory binomial-coefficients

An interesting property of binomial coefficients that I couldn't prove

binomial-coefficients exponentiation

Is there a closed form or approximation to $\sum_{i=0}^n\binom{\binom{n}{i}}{i}$

combinatorics discrete-mathematics binomial-coefficients

Evaluate $\sum_{r=0}^n 2^{n-r} \binom{n+r}{r}$

sequences-and-series contest-math binomial-coefficients

Given a finite set U, how can we enumerate all subsets of U that have an odd number of elements [duplicate]

summation binomial-coefficients

New Year Maths 2015

combinatorics summation binomial-coefficients recreational-mathematics products

Why the $GCD$ of any two consecutive Fibonacci numbers is $1$?

elementary-number-theory binomial-coefficients divisibility fibonacci-numbers gcd-and-lcm

How to prove binomial coefficient $ {2^n \choose k} $ is even number?

combinatorics binomial-coefficients

power series with binomial coefficient

real-analysis power-series binomial-coefficients

Determine $\lim\limits_{n \to \infty}{{n} \choose {\frac{n}{2}}}\frac{1}{2^n}$, where each $n$ is even

probability limits binomial-coefficients

Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$

combinatorics summation binomial-coefficients

Proof of equality $\sum_{k=0}^{m}k^n = \sum_{k=0}^{n}k!{m+1\choose k+1} \left\{^n_k \right\} $ by induction

summation induction binomial-coefficients

Is there a closed form for $\sum_{n=0}^{\infty}{2^{n+1}\over {2n \choose n}}\cdot\left({2n-1\over 2n+1}\right)^2?$

sequences-and-series binomial-coefficients closed-form

Show that if $\prod\limits_{k=1}^{n}(x+a_k)=\sum\limits_{k=0}^{n} {n\choose k}a^k_kx^{n-k}$ then $a_1=a_2=a_3=....=a_{n-1}=a_n$

sequences-and-series binomial-coefficients

Summation simplification $\sum_{k=0}^{n} \binom{2n}{k}^2$

binomial-coefficients summation

Prove that $\inf\limits_{n\in\mathbb N}\sum\limits_{k=0}^{p}\lvert\sin{(n+k)^p}\rvert>0$

calculus sequences-and-series analysis inequality binomial-coefficients