# Well, that was unexpected

Calculus Level 5

Let $$S=0$$.

Pick a random real number $$k$$ from a uniform distribution on $$[0,1]$$. Then add $$k$$ to $$S$$: if $$S<1$$ then repeat the process and add another number. If $$S\ge1$$ then the process ends.

What is the expected value of $$S$$?

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