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Newton binomial expansion

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#binomial-coefficients
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Justify an approximation of $\sum_{n=1}^\infty G_n/\binom{\frac{n}{2}+\frac{1}{2}}{\frac{n}{2}}$, where $G_n$ denotes the Gregory coefficients

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#real-analysis #sequences-and-series #asymptotics #binomial-coefficients #analytic-number-theory
123
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Solving an equation involving binomial coefficients

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#algebra-precalculus #binomial-coefficients
671
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Asymptotics for partial sum of product of binomial coefficients

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#discrete-mathematics #reference-request #asymptotics #binomial-coefficients
69
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What is wrong with this proof about a sum of binomial coefficients?

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#proof-verification #binomial-coefficients
116
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Find sum of nasty series containing Binomial Coefficients

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#binomial-coefficients #binomial-theorem
381
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Alternating Binomial Series Summation.

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#binomial-coefficients
544
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$x+\frac{1}{x}$ is an integer

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#proof-verification #induction #binomial-coefficients
75
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Finding value of $S-T$ in $2$ binomial sum.

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#binomial-coefficients
59
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how to reduce $(1-\alpha)^{T-i}$ into a sum

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#abstract-algebra #combinatorics #polynomials #binomial-coefficients #multinomial-coefficients
58
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Binomial Theorem Question $1+(1+x)+(1+x)^2+\dots+(1+x)^n$

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#binomial-coefficients #binomial-theorem
1.5k
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Probabilities with unfair dice.

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#probability #binomial-coefficients
1.1k
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In the expansion of $(ax+b)^{2000}$, where a and b are relativel prime integers, the coefficients of $x^2$ and $x^3$ are equal. What is (a, b)?

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#binomial-coefficients
251
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Remainder when $\binom{2018}{1009}$ is divided by $ 2017^2?$

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#algebra-precalculus #binomial-coefficients #divisibility
116
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Formulas involving pairs of coefficients of expansion of $(1+x+x^2)^n$

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#binomial-coefficients

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