(a) If an+1 = an/(an+1) prove that an = ao/(nao+1) for all n ≥ 0. OL

Let x ER and x > −1. Prove that (1 + x)” ≥ 1 + nx for every positive integer n.

Prove that (-1+i3) + (-1 - if3)" has either the value 271 er the value -2" if n is ary n+1 Interer (positive Zero).

Let q1, q2, q3, . . . be defined by q1 = 2, qn = 3qn−1 − 1 for n ≥ 2. Show byinduction that for all n ≥ 1, qn =1/2(3n + 1).

Given f(x)=e*, g(x)=5* , and h(x) =g(x)/f{x), find h"(x). A) 5*e*(In5+1)² B) 5*e*(In 5–1)² C) 5*e*(In 5)² D) -x(x-1)5*-2²n5)²

Let X= {ne 7 /n=2k for some odd integer & f F = {ne z/n=4k for some integer *} E = {nEX/ n is even } 1. Prove that Fc I 2. Prove that XEnF