Lesson 25a - Ratio and Root Test

# Bycomparison testouroriginalseriesmustalsoconverge an

This preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: ve: an L This means we get: nk nk | an | Ln The series on the right is a geometric series, and converges as L &lt; 1. By comparison test, our original series must also converge. | an | Ln For L &gt; 1, the proof is identical except we have , but the series nk nk on the right is divergent (geometric series L &gt; 1). By comparison, the original diverges as well. Strategy for Using Ratio/Root Test The ratio test should typically be used when we have the following in our series: 1. 2. Exponentials and polynomials as our highest terms. Factorials (recall that a factorial means n! = (n)(n‐1)(n‐2)…(3)(2)(1) ) The root test should typically be used when we have the following in our series: 1. f(n...
View Full Document

## This note was uploaded on 02/07/2014 for the course MATH 1004 taught by Professor Mark during the Summer '00 term at Carleton CA.

Ask a homework question - tutors are online