1. The problem statement, all variables and given/known data Use the definition of convergence to prove that lim n→∞ (1/2)^n=0 The definition of convergence says |a_n-L|<ε 2. Relevant equations 3. The attempt at a solution As I understand it: |(1/2)^n-0|<ε |(1/2)|^n<ε then I need to solve for n? n>(ln(ε))/ln(|1/2|) Then I choose N=(ln(ε))/ln(|1/2|) but I don't understand why. n>N>(ln(ε))/ln(|1/2|)?? Given that ε>0 and n>N then n>(ln(ε))/ln(|1/2|) then solving for ε I get the statement |(1/2)|^n<ε from above. Thanks!