lec 18

# lec 18 - Tuesday February 7 − Lecture 18 Tests for...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Tuesday, February 7 − Lecture 18: Tests for convergence of series : Comparison test. (Refers to Section 8.4 in your text) After having practiced the problems associated to the concepts of this lecture the student should be able to : Apply the comparison test to determine convergence or divergence of a series, show a reasonable error bound for the value of a series known to converge by the integral test or by the fact it is a geometric series. 18.1 Theorem − The Comparison test . Let be two series such that 0 ≤ a i ≤ b i for all i . Then the following statements hold true : Proof: Part I : In this part the Monotone convergence (sequence) theorem is invoked. Given: Since 0 ≤ a i ≤ b i for all i . So the sequences { A n } and { B n } are such that A n ≤ B n for all n . We are also given that the sequence { B n } converges, say to L . Required to show: That the sequence { A n } must converge to some number. Part II : Given: The sequences { A n } and { B n } are such that A n ≤ B n for all n and that the...
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

lec 18 - Tuesday February 7 − Lecture 18 Tests for...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online