<t>The idea would be more like this.(*) E[X(i)] = E[E[X(i)|X(i-1)]] = 1/2E[X(i-1)^a]Then what you want to do is recognise for a rv Y distributed uniformly over [0,u], E[Y^a] = 1/(1+a)Y^a, and keep applying the Tower law as we did in (*). With a bit of persistence (lacking here) you should get what y...