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simple form of binomial coefficient and product

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Find the summation of the following sequence

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#sequences-and-series #binomial-coefficients #combinations
283
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Coefficient of $x^2$ in $(x+\frac 2x)^6$

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Evaluation of ratio of two binomial expression

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466
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How to show that $\sum_{k} (-1)^k{{a+b}\choose{a+k}}{{b+c}\choose{b+k}}{{c+a}\choose{c+k}} = \frac{(a+b+c)!}{a!b!c!}$

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#combinatorics #summation #binomial-coefficients #factorial #multinomial-coefficients
469
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Evaluate$\sum_{n=0}^\infty\binom{3n}{n}x^n$

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#sequences-and-series #algebra-precalculus #binomial-coefficients
387
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A proof for the identity $\sum_{n=r}^{\infty} {n \choose r}^{-1} = \frac{r}{r-1}$

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#sequences-and-series #combinatorics #binomial-coefficients
124
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finding $\mathop{\sum\sum}_{0 \leq i < j\leq n}(i+j)\binom{n}{i}\binom{n}{j}$

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#binomial-coefficients
113
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How to solve this binomial expansion?

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143
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Binomial Series Expansion

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#binomial-coefficients #binomial-theorem
244
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Find the sum of $\binom{2016}{4} + \binom{2016}{8} +\binom{2016}{12} + \dots + \binom{2016}{2016}$

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#combinatorics #summation #binomial-coefficients
39
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expanding exponential of inverse

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#binomial-coefficients
54
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On the convergence of a seemingly tricky sequence

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#sequences-and-series #convergence-divergence #binomial-coefficients
452
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Series with Binomial Coefficients

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#sequences-and-series #summation #power-series #binomial-coefficients
704
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Series with Double Binomial Coefficients

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