Answer Happy

PLEASE JUST ANSWER NUMBER 6, THE NUMBER 5 WILL BE THE GUIDE TOCOMPARISON.
5. Let c be a number such that |c| < 1. Show that |c| can be expressed as|c] = 1/(1+d), where d > 0. Then use the Binomial Formula to show that |c²| ≤ for every index n. 6. a. Use Exercise 5 and the Comparison Lemma (Lemma 2.9) to obtain another proof that if |c|< 1, then limn→∞ c" = 0. b. Use Exercise 5 and the Comparison Lemma to prove that lim,→∞ √nc" = 0. Is the sequence {√√nc"} necessarily monotone? 1 1+nd 1 dn