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Question Number 182890 by Frix last updated on 16/Dec/22

Find the formula in terms of n  S_n =Σ_(j=1) ^∞  (1/(Π_(k=0) ^n  (j+k)))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{formula}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{n} \\ $$$${S}_{{n}} =\underset{{j}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\underset{{k}=\mathrm{0}} {\overset{{n}} {\prod}}\:\left({j}+{k}\right)} \\ $$

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