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Can we show that $\frac{\sum_{j=1}^n j^2\cdot j!}{99}$ generates only finite many primes?

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#elementary-number-theory #summation #prime-numbers #recreational-mathematics #factorial
34
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Falling and rising factorial series identity

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#real-analysis #power-series #factorial #products
79
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Permutations and combinations - divisibility of a factorial

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#permutations #factorial
107
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convergence of $\sum_{n=2}^{\infty}\frac{(n+1)!(n+1)^{n-1}}{n^{2n}}$

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#real-analysis #sequences-and-series #limits #factorial #limits-without-lhopital
120
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Limit of $\lim \limits_{x \rightarrow \infty}\frac{(x!)^n}{(ax)!}$

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#limits #factorial
4.3k
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Solving for $r$ in ${12\choose{r}}=924$

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#combinations #factorial
218
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Sum concerning Catalan triangle and binomials

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#summation #binomial-coefficients #factorial #catalan-numbers
541
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How to simplify a fraction involving factorials

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#algebra-precalculus #factorial
295
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Need help finding a closed form for complicated sum

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#sequences-and-series #summation #binomial-coefficients #factorial #closed-form
210
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What condition does a recursive function have to fulfill to be well defined?

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#functions #factorial
298
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Sum problem involving Factorials

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#summation #binomial-coefficients #factorial
877
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How to calculate what this power series converges against? (double factorials)

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#limits #convergence-divergence #power-series #factorial
134
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Question about Binomial Sums

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#combinatorics #algebra-precalculus #summation #binomial-coefficients #factorial
150
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Is there a closed form for this sequence?

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#permutations #factorial #binomial-theorem
764
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Showing $\binom{2n}{n} = (-4)^n \binom{-1/2}{n}$

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#binomial-coefficients #factorial

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