{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture 8-5

# Lecture 8-5 - lim n →∞ n √ n = 3 Examples Determine...

This preview shows pages 1–5. Sign up to view the full content.

8.5 - The Ratio and Root Tests The Ratio Test Suppose a n is a series of positive terms and lim n →∞ a n +1 a n = L. Then, 1. 2. 3. Note: Examples Determine whether the following series converge or diverge. 1. X n =1 5 n n 3 1

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

View Full Document
2. X n =1 n 2 n ( n + 1)! 3 n n ! 3. X n =1 n + 2 5 n 2 + 3 2
The Root Test Let a n be such that a n 0 for all n N , where N is some positive integer. Suppose lim n →∞ n a n = ρ. Then, 1. 2. 3. Note: Helpful limit to know when using the Root Test

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: lim n →∞ n √ n = 3 Examples Determine whether the following series converge or diverge. 1. ∞ X n =1 (ln n ) n n n 2. ∞ X n =1 10 n n 10 4 Do. Determine if the following series converge or diverge. 1. ∞ X n =1 n ± 1 2 ² n 2. ∞ X n =1 n ! ln n n ( n + 2)! 5...
View Full Document

{[ snackBarMessage ]}