1. The problem statement, all variables and given/known data There are two separate series I'm having trouble with, although they're related. The scenario: Roll a fair die until a six comes up. pmf = (5/6)^(x-1) * (1/6) So first, show the sum from 1 to infinity of p(x) =1 Next, determine P(X=1,3,5,7,...) that it will appear on an odd roll. 2. Relevant equations I'm trying to prove 1=sum (5/6)^(x-1) * (1/6) and sum (5/6)^(2x-1) * (1/6) = ? 3. The attempt at a solution For the first, I tried induction but got lost along the way. The second, the back of the book states = 6/11 but getting there sends me back to computing the first series.