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November 17th, 2017, 09:51 PM   #1
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Binomial Sum

Prove that $\displaystyle \displaystyle \binom{n}{1}-\left(1+\frac{1}{2}\right)\binom{n}{2}+\left(1+ \frac{1}{2}+\frac{1}{3}\right)\binom{n}{3}+\cdots \cdots \cdots +(-1)^n\left(1+\frac{1}{2}+\frac{1}{3}+\cdots \cdots +\frac{1}{n}\right)=\frac{1}{n}$

Last edited by panky; November 17th, 2017 at 09:53 PM.
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