Let [tex] A_i = \frac{1}{n}\cdot \frac{(-1)^{n-i}}{i!\cdot(n-i)!} \int_{0}^{n} \frac{t(t-1)...(t-n)}{t-i}dt[/tex](adsbygoogle = window.adsbygoogle || []).push({});

I need to prove

[tex] \sum_{i=0}^{n} A_i = 1 [/tex].

I tried tinkering with the equasion but I'm really at a loss what to do with the integral. I'd appreciate any help.

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# Need help with proof

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