November 17th, 2017, 08:51 PM  #1 
Senior Member Joined: Jul 2011 Posts: 405 Thanks: 16  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 08:53 PM. 

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