1. The problem statement, all variables and given/known data Suppose that Pr(X = 0) = Pr(X = 1), Pr(X = k + 1) = (1/k)Pr(X = k), k = 1,2,3,··· Find Pr(0). 2. Relevant equations 3. The attempt at a solution Ok I started with k = 1 and went to k = 5. The pattern I noticed is For k=n we have p(X=n+1) = (1/2)(1/3)(1/4)...(1/n)p(X=1) = (1/n!)p(X=1) Let k go to inf We have Ʃ (1/n!) p(X=1) The above summation equal 1 by probability axiom. We get p(X=1) = Ʃ 1/n! It is known that ex = Ʃ xn/n! Where 0≤n<∞ In this case we are starting from 1 so we must reindex to get ex = 1 + Ʃ xn/n! We then have P(X=1) = 1/(Ʃ 1/n!) = 1/e-1 Since p(X=0) = p(X=1) is given we end up with p(X=0) = 1/e-1 But the answer is 1/e+1. I sense I am close but I am messing up something with the reindexing maybe?