# Expected Random Sum Above 1

Starting with $$S= 0$$, you choose a number between $$0$$ and $$1$$ at random and add it to $$S$$. If $$S< 1$$, you repeat and choose a number between $$0$$ and $$1$$ at random and add it to $$S$$. If $$S \geq 1$$, you stop.

If the expected value of $$S$$ when you stop is denoted by $$E[S]$$, what is the integer closest to $\frac { 200 \times E[S] }{ e^2 } ?$

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