How could I go about proving this summation of a rising factorial? – math.stackexchange.com

How could I go about proving this summation of a rising factorial? – math.stackexchange.com

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$$\sum_{r=1}^{n}r(r+1)(r+2)...(r+p-1) = \frac{1}{p+1}n(n+1)(n+2)...(n+p)$$ So I get how to do this with limited terms, like r(r+1) just ends up with some summations of r, r^2 and onward, but how ...

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