1. The problem statement, all variables and given/known data Prove that L1 + 2L2 + 4L3 + 8L4 + ... + 2n-1L1 = 2nFn+1 -1. 2. Relevant equations The Fibonacci numbers denoted by Fn is defined as follows: F1 = 1 , F2 = 1 , F3 = 2 , F4 = 3 , F5 = 5 Fn = Fn-1 + Fn-2 The Lucas numbers are defined as: Ln = Fn+1 + Fn-1 3. The attempt at a solution I have attempted to solve this as follows (which I'm sure is wrong): Assume it's true for n = k and for k + 1: 2kFk+1 -1 + 2k+1Lk+1 => 2kFk+1 + 2k+1(Fk+2 + Fk) => 2k(Fk+1 + 2(Fk+2 + Fk)) But from here, I'm not quite sure how to proceed (if this is in fact, which i doubt, the right way to approach this problem). Also, note that I'm quite inexperienced when it comes to number theory so this may in fact be a trivially easy problem, but I'm having a hard time to see how to correctly approach these types of problems. Thanks in advance!