My Math Forum 1, 2, 3... sum/product summation

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 May 21st, 2019, 08:53 PM #1 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 464 Thanks: 29 Math Focus: Number theory 1, 2, 3... sum/product summation 1/1+(1+2)/(1*2)+(1+2+3)/(1*2*3)+(1+2+3+4)/(1*2*3*4)...=?
 May 22nd, 2019, 03:28 AM #2 Newbie   Joined: Sep 2017 From: Belgium Posts: 19 Thanks: 7 $\frac{3}{2}e$ by using this $\sum_{k=0}^\infty{k+2\choose k}\frac{1}{(k+1)!}$ $\sum_{k=0}^\infty\frac{k+2}{2\cdot k!}$ $\sum_{k=0}^\infty\frac{k}{2\cdot k!}+\frac{1}{k!}$ and this $\sum_{k=0}^\infty\frac{x^k}{k!}=e^x$ Thanks from topsquark and Loren

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