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coefficient $x ^ n$ in development

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#binomial-coefficients #binomial-theorem
194
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Number of ways to express sum.

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#combinatorics #discrete-mathematics #generating-functions #binomial-theorem
178
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Evaluate: $\sum_{j=0}^{k}\sum_{i=0}^{j}{k \choose j}^2{k \choose i}$

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#sequences-and-series #binomial-theorem
37
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Need help expanding this negative binomial expanison

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#binomial-theorem #negative-binomial
134
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If $C_0, C_1, C_2, .., C_n$ are the binomial coefficients in the expansion of $(1+x)^n$

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#calculus #integration #derivatives #binomial-coefficients #binomial-theorem
218
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Are there any power identities which don't belong to this list?

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#combinatorics #number-theory #soft-question #binomial-coefficients #binomial-theorem
130
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Combinatorial identities, check the asymptotic behavior.

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#combinatorics #asymptotics #binomial-theorem
93
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Binomial probability question!

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#probability #binomial-theorem
3.6k
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Using the binomial expansion to approximate a square root.

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#proof-verification #binomial-theorem
103
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How to simplify this sum

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#combinatorics #binomial-theorem #binomial-distribution
109
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To find the sum: $\frac {1}{n!} \sum \binom {n}{2+3r} x^{1+r}$

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#sequences-and-series #summation #binomial-theorem #roots-of-unity
3.1k
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Simple Proof of Binomial Theorem for Negative Integer Powers

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#proof-verification #induction #integers #binomial-theorem
58
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What is the intermediate step in this negative binomial proof?

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#markov-chains #factorial #binomial-theorem
99
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Summing Up Binomial Coefficients

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#combinatorics #binomial-coefficients #binomial-theorem
477
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Help on proof of $\binom{n}{0}^2 + \binom{n}{1}^2 + ... + \binom{n}{n}^2 = \binom{2n}{n}$

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#discrete-mathematics #binomial-coefficients #binomial-theorem

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