This is one problem but it has two sections. I hope you can help me. This is the last problem I need help with so I would be grateful if it's quick. But thanks anyway.

Problem 6. (10 points). Let us say that a sequence of real numbers (br ) is a "good" sequence if for every & > 0 there exists / such that n 2 N = 10n+1 - bul E. 2 (1) Let n bn = > 1=1 Show that (b,) is a " good" sequence. (2) Show that if (b,) is a Cauchy sequence then it is "good". Is every "good" sequence Cauchy? Prove your