(5) Prove that if a > 1, a 7E 0 then (1 + a)m > 1 + ma for any integer m > 1 (this is one of Bernoulli's inequalities). [10 marks] (6) Let a > 1 and let n be a positive integer. Prove that . _ (Hint: you may use 3:\" 1 = (a: _. 1)(:.c\"\"'_1 + $1123 + - - - + a: + 1).) [10 marks]