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May 21st, 2019, 08:53 PM   #1
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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)...=?
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May 22nd, 2019, 03:28 AM   #2
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$\frac{3}{2}e$
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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