1. Math
  2. Advanced Math
  3. let an be a sequence of nonzero real numbers such...

Question: let an be a sequence of nonzero real numbers such...

Question details

Let (an) be a sequence of nonzero real numbers such that L= lim lemti n-00an exists. (a) (Ratio Test) Prove that i, iflimlan+1| < 1, then Στοι an is absolutely convergent, and n-an n+1 an > 1, then Ση an is divergent. ii. if lim n→ool (b) Consider the power series i. Prove that if L 0, then for each x E (c-1/L,c+ 1/L), the power series (1) is absolutely convergent. ii. Prove that if L-0, then for each real number x, the power series (1) is absolutely convergent.

Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution