Sum of random number of variables

Let $$x_1,x_2,x_3, \ldots$$ be sequence of numbers randomly picked from the interval $$[0,1]$$ with uniform distribution. define $S=x_1+\cdots+x_n\mid x_1+\cdots +x_{n}\geq 1 \land x_1+\cdots+x_{n-1}<1.$

The expected value $$E\left[S\right]$$ can be written as $$\dfrac{ae}{b}$$, where $$a$$ and $$b$$ are coprime integers. Find $$a+b$$

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