3.15 Determine the order relation of the following sequences an and bn:

(i) an = c0+c1n+· · ·+cknk, bn = an for any positive integer k anda > 1, where c1, . . . , ck are constants.

(ii) an = {log(n)}1− , bn = log(nδ) for any 0 <  < 1 and δ > 0.

(iii) an = exp[{log(n)} ], bn = nδ for any 0 <  < 1 and δ > 0.

(iv) an = (n/a)n, bn = n!, where a > 0. (Note: Depending on the value of

a, the conclusion may be different.)