Show that n^2 < 2^n for n > 5. Solution by induction.: Assume the result for n. (ie) n^2 < 2^n. For n+1, consider, (n+1)^2 - n^2 = 2n+1<2^n for n >2. Using induction (n+1)^2 < n^2+2^n < 2^n + 2^n =2(2^n) =2^(n+1). This true for n > 5 and equality holds if n = 4.