Plz give me an example for this theorem

Or COurse, we canno use the previous theorem when dealing with infinite limits. Theorem. Let {a} and {b, be sequence such that lim a, = +oo and lim b > 0. Then lim a b = +o0. Proof. Let M> 0. Choose a real number m so that 0 < m < lim b Whether lim b, = +o Or not, there exists N, so that if n > N, then b, > m. Since lim a, = +o there is an N, so that if n> N, then