Expected Random Sum Above 1

Probability Level 5

Starting with S=0S= 0 , you choose a number between 00 and 11 at random and add it to SS. If S<1 S< 1 , you repeat and choose a number between 00 and 11 at random and add it to SS. If S1S \geq 1 , you stop.

If the expected value of SS when you stop is denoted by E[S] E[S], what is the integer closest to 200×E[S]e2? \frac { 200 \times E[S] }{ e^2 } ?

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