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I have fixed my OP to include that important piece of information. Thank you for catching this error.$$\sum_{k=1}^{j}\underbrace{\phantom{e^{-x^{2}}}}_{\text{What goes here?}}$$
$1-\dfrac {1}{1+2+3+----+n}=1-\dfrac {2}{n(n+1)}$Prove that:
\(\displaystyle \prod_{j=2}^n\left(1-\frac{1}{\sum\limits_{k=1}^j(k)} \right)=\frac{n+2}{3n}\)