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A combinatorial identity generalizing identity (3.111) from Gould's book

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#combinatorics #summation #binomial-coefficients
61
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How to compute $\displaystyle\sum_{k\equiv 1\!\!\pmod{\!4}}\!\!\binom{2014}{k}$?

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#algebra-precalculus #binomial-coefficients #binomial-theorem
80
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Issue to identify binomial distribution

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#probability #probability-distributions #binomial-coefficients
84
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Simplify the sum

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#combinatorics #summation #binomial-coefficients
166
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$\sum_{n=0}^{\infty}\binom{2n}{n}\frac{1}{2^{2n}}$

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#sequences-and-series #binomial-coefficients #contour-integration
2.6k
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Induction proof: sum of binomial coefficients

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#induction #binomial-coefficients
120
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Sum of binomial coefficients and powers

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#combinatorics #summation #binomial-coefficients
1.5k
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Negative binomial theorem

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#combinatorics #proof-verification #binomial-coefficients #binomial-theorem
69
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Can a certain polynomial have all its coefficients in some basis divisible by a prime $p$?

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#polynomials #binomial-coefficients
69
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Recovering the coefficients $b_r$ of the binomial sum $\sum_{r=0}^n\binom{n}rb_r$

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#elementary-number-theory #summation #binomial-coefficients
155
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Differentiation of a binomial-like sum with respect to m (total number of trials)?

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#calculus #combinatorics #algebra-precalculus #statistics #binomial-coefficients
181
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Prove Binom Sum $\sum_{k=0}^n(-1)^k \binom{n}{k} = 0$

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#summation #binomial-coefficients
322
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Counting elements in cartesian power with plurality + pattern constraints

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#combinatorics #permutations #binomial-coefficients #combinations #combinatorics-on-words
741
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Even/Odd Binomial Coefficients

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#number-theory #elementary-number-theory #prime-numbers #binomial-coefficients
206
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Binomial series after using binomial identity

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#binomial-coefficients

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