Oggy
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Let 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
I need to prove
\sum_{i=0}^{n} A_i = 1.
I tried tinkering with the equation but I'm really at a loss what to do with the integral. I'd appreciate any help.
I need to prove
\sum_{i=0}^{n} A_i = 1.
I tried tinkering with the equation but I'm really at a loss what to do with the integral. I'd appreciate any help.
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