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Solve for $x$ and $y$: $\sum_{n=3}^{n=10} {^nC_3}\cdot{^{14-n}C_4}={^xC_y}$.

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#sequences-and-series #combinatorics #binomial-theorem
138
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What's the rule for Pascal's Triangle?

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#binomial-theorem
87
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Can I show that $n \cdot \binom{n-1}{n}=0$?

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#combinatorics #discrete-mathematics #binomial-coefficients #binomial-theorem
107
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Binomial/combinatorics summation proof question

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#combinatorics #summation #binomial-coefficients #binomial-theorem
38
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A question on binomial expansion

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#binomial-coefficients #binomial-theorem
73
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What is the sum of the coefficients of the terms containing $x^2t^3$ in the given expansion.

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#combinatorics #solution-verification #binomial-coefficients #binomial-theorem
387
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Proof of binomial series in the case N is a real number

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#sequences-and-series #binomial-theorem
100
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Proof of an equation with the aid of Laguerre functions?

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#combinatorics #power-series #generating-functions #binomial-theorem #laguerre-polynomials
60
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How can I prove that $(x)^{(x+1)} > (x + 1) ^x$ for integer values of $x$ by induction?

Published on
#exponentiation #binomial-theorem
78
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Is there any simple form for sum of even items of $(1+x)^n$

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#sequences-and-series #summation #binomial-theorem
190
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Approximate roots using the binomial series.

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#approximation #radicals #binomial-theorem
153
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A very good question on binomial theorem .

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#number-theory #elementary-number-theory #permutations #binomial-coefficients #binomial-theorem
41
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Why my generalized term does not give the correct answer

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#binomial-theorem
227
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Is it possible to determine the number of terms in a multinomial expansion, if all terms are exponents of $x$?

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#combinatorics #binomial-theorem #multinomial-theorem
290
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Simplifying $(1+i)^n-(1-i)^n$

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#complex-numbers #binomial-theorem

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