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 \(S\)?

Credit to a teacher for showing me this problem

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