1. The problem statement, all variables and given/known data Prove that 1/(1-x) = 1 + x + x2 + x3 + ... + xn/(1-x) for n>=2 2. Relevant equations 3. The attempt at a solution I'm not really all that sure how to begin. The base case would be 1/(1-x) = x2/(1-x) and the induction hypothesis would be 1/(1-x) = 1 + x + x2 + x3 + ... + xn/(1-x) but I don't know what the n+1 case is and how to prove that it holds. I guess the n+1 case would logically be 1/(1-x) = 1 + x + x2 + x3 + ... + xn/(1-x) + xn+1/(x-1), but I don't know how to show algebraically that the left hand side equals the right hand side.