Define a sequence of real numbers (2) by 3 21 I = (a) (b) (c) (d) and In+1 =(+2) for n> 1. Show that 1 2 for all ne N. Show that +1 =(-1)(-2) for all n N. Show that the sequence (zn) is monotone. Explain why the sequence converges and find its limit, justifying your reasoning carefully.