(1.7) Geometric growth. Suppose (an : n 2) is a sequence of positive numbers that satisfy \"3:1 ) L > 1 as n ) oo. (a) Show, for some N, that (247:1 Z L for all n 2 N. (b) Use induction to show that aN+n 2 (m (%)l1 for n 2 1. Hence conclude, by comparison, that an > 00 as n > 00. (c) Apply this to the sequence on = \"21% to give another proof that an > 00 (that we already know since exponentials beat polynomials)