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The series$\sum\limits_{n=1}^{\infty}(\frac{(2n-1)!!}{(2n)!!})^p$ converges if and only if $p>2$

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#sequences-and-series #analysis #convergence-divergence #binomial-coefficients
222
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Evaluate the Binomial Sum

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#calculus #combinatorics #binomial-coefficients #binomial-theorem
287
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sum of alternating binomial

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#combinatorics #summation #binomial-coefficients
56
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Could someone please explain the steps to solve an equation like this?

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#binomial-coefficients
1.1k
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Binomial Expansions No calculator

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#binomial-coefficients #binomial-distribution
295
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Divisibility of a binomial coefficient by a prime

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#prime-numbers #binomial-coefficients #divisibility
211
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Periodic sequences resulting from a summation over the Thue–Morse sequence

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#sequences-and-series #combinatorics #number-theory #discrete-mathematics #binomial-coefficients
14.2k
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How to find the numerically greatest term in the expansion of $(3x+5y)^{12}$ when $x=\frac12,y=\frac43$

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#binomial-coefficients #binomial-theorem
116
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On the integral $-\int\log\left(\binom{1-x}{6}+\binom{x}{6}\right)dx$, and its definite integral over the unit interval

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#integration #definite-integrals #binomial-coefficients #closed-form
134
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What is the relationship between sums of powers of $n$ and the stirling numbers?

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#number-theory #binomial-coefficients #stirling-numbers
83
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Show that $\binom{2n}{n}\geq2^n$ for all $n\in\mathbb{N}_0$.

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#algebra-precalculus #proof-verification #proof-writing #induction #binomial-coefficients
136
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Closed form for $\sum\limits_{k=0}^{b}k^na^k$

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#binomial-coefficients #closed-form #stirling-numbers #bernoulli-numbers
567
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Finding Tight bound for Binomial Coefficient inequality

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#combinatorics #inequality #binomial-coefficients
67
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Calculate sum with binom. coef.

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#summation #binomial-coefficients
177
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Divisibility of Sum of Equally Spaced Binomial Coefficients

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#sequences-and-series #combinatorics #number-theory #summation #binomial-coefficients

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