It isn't a homework problem but I think I better post it here instead of Mathematics forum, since it belongs to "exam help". Prove that for any positive real numbers a and b, lim [(an+b)1/n-1] = 0 n->inf I don't need to use things like |a-b|<epsilon. A simple way will do. I know it's an easy question but I don't know where to start. Could someone please help.