The function fis defined by fixe*-1-x (i) Find the minimum value of f. (ii) Prove that e* 1 + x for all real values of x. Use the principle of mathematical induction to prove that (1+Y)(1+2)(+)... +)=n+1 n for all integers n 1. Use the results of parts (a) and (b) to prove that 1 1 (1+-+-++. 23 e n > n.