I don't even know how to proceed. Please help me with this. 

(Original at <https://i.stack.imgur.com/DRIX8.jpg>)

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> Consider all non-empty subsets of the set $\{1, 2, \ldots, n\}$. For every such subset, we find the product of the reciprocals of each of its elements. Denote the sum of all these products as $S\_n$. For example,
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> 
> $$
> S\_3 = \frac11 + \frac12 + \frac13
>  + \frac{1}{1\cdot2} + \frac{1}{1\cdot3} + \frac{1}{2\cdot3}
>  + \frac{1}{1\cdot2\cdot3}
> $$
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> (a) Show that $S\_n = \frac1n + \left(1 + \frac1n\right)S\_{n-1}$.
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> (b) Hence or otherwise, deduce that $S\_n = n$. 
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