# 2009-20 Expectation

Let en be the expect value of the product x1x2 …xn where x1 is chosen uniformly at random in (0,1) and xk is chosen uniformly at random in (xk-1,1) for k=2,3,…,n. Prove that $$\displaystyle \lim_{n\to \infty} e_n=\frac1e$$.

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