1. The problem statement, all variables and given/known data Show that the if lim bn = b exists that limsup bn=b. 3. The attempt at a solution Let limsup = L and lim = b We know for all n sufficiently large |bn-b|<ε |bn| < b+ε Therefore L ≤ b+ε and |bn| < L ≤ b+ε I'm trying to get |bn-L|<ε or |L-b|<ε both of which I believe imply that b=L. The problem is I can't get my absolute value signs to be correct.