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This tag is used if a reference is needed in a paper or textbook on a specific result.
24
votes
Proofs without words
(I'd post this as a comment to Mariano Suárez-Alvarez, but I've not enough rep). From a ME thread.
$$\sum_{k=1}^n (-1)^{n-k} k^2 = {n+1 \choose 2} = \sum_{k=1}^n \; k = \frac{(n+1) \; n}{2}$$
5
votes
Accepted
Understanding a particular approximation for Stirling's number of the second kind
I cannot provide you with a reference, but I can sketch with my own derivation (I have a draft somewhere...).
First, let $X$ be a zero-truncated multinomial $(n,k)$ random variable (we throw $n$ ball …