Why does $\sum\limits_{k=1}^\infty \lfloor m/(n^k)\rfloor$ give you the number of times that $n$ divides $m!$?
5206
Highest power of a prime $p$ dividing $N!$
11389
What is $\lim_{n\to \infty}\sum_{k=1}^n \left(\frac{k}{n}\right)^n$?
634
Closed form formula for $\sum\limits_{k=1}^n k^k$
79836
Proof for $\left\lfloor\frac 1j\left\lfloor\frac nk\right\rfloor\right\rfloor=\left\lfloor\frac n{jk}\right\rfloor$
17713
What's the value of $\sum\limits_{k=1}^{\infty}\frac{k^2}{k!}$?
76828
Evaluating $\sum_{i = 0}^{\lfloor n/2 \rfloor} {n \choose 2i}p^{2i}(1 - p)^{n - 2i}$
101017
What is the sum of $\sum\limits_{i=1}^{n}ip^i$?
128200
Sequence sum question: $\sum_{n=0}^{\infty}nk^n$
147887
When do we have $ \lim_{n\to\infty}\sum_{k=1}^{n^2}\frac{n^{r-1}}{n^r+k^r}0$?
123955
How to compute $\sum\limits_{k=0}^n (-1)^k{2n-k\choose k}$?
118436
Identifying the series $\sum\limits_{k=-\infty}^{\infty} 2^k x^{2^k}$
29609
Limits involving factorials $\lim_{N\to\infty} \frac{N!}{(N-k)!N^{k}}$
111524
Information on the sum $\sum_{n=1}^\infty \frac{\log n}{n!}$
142338
Prove that $\lfloor\frac{n+1}{2}\rfloor+\lfloor\frac{n+2}{4}\rfloor+\lfloor\frac{n+4}{8}\rfloor+\lfloor\frac{n+8}{16}\rfloor+ \dots=n$
26837
Limit of the sequence $\{n^n/n!\}$, is this sequence bounded, convergent and eventually monotonic?
27844
How do we prove that $\lfloor0.999\cdots\rfloor = \lfloor 1 \rfloor$?
153231
Why does $\sum_1^\infty \frac1{n^3}=\frac52\sum_1^\infty\frac{(-1)^{n-1}}{n^3\binom{2n}{n}}$?