# 12-4 - 1 12.4: Examples Determine if the series converges...

This preview shows pages 1–4. Sign up to view the full content.

12.4: The Comparison Tests The Comparison Test allows us to determine the con- vergence or divergence of a series a n by comparing it to a series b n we already understand. Theorem (The Comparison Test) . Suppose that a n and b n are series with positive terms. 1. If b n is convergent and a n b n for all n , then a n is also convergent. 2. If b n is divergent and a n b n for all n , then a n is also divergent. The geometric series, p -series, and harmonic series are often good candidates to use when trying to ﬁnd a series for comparison since we understand the convergence/divergence for each of these series.

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

View Full Document

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: 1 12.4: Examples Determine if the series converges or diverges. 1. ∑ ∞ n =1 1 1+2 n 2. ∑ ∞ n =1 1 √ n 2-1 3. ∑ ∞ n =1 n-1 n 4 n 2 12.4: The Comparison Tests Theorem (The Limit Comparison Test) . Suppose that ∑ a n and ∑ b n are series with positive terms. If lim n →∞ a n b n = c where c is a ﬁnite number and c > 0, then either both series converge or both diverge. 3 12.4: Examples Determine if the series converges or diverges. 1. ∑ ∞ n =1 1 2 n-1 2. ∑ ∞ n =1 √ n +2 2 n 2 + n +1 4...
View Full Document

## This note was uploaded on 04/04/2011 for the course MATH 408 L taught by Professor Zheng during the Fall '10 term at University of Texas.

### Page1 / 4

12-4 - 1 12.4: Examples Determine if the series converges...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online