{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lesson 20a - Comparison Test

# Lesson 20a - Comparison Test - ComparisonTest a n 1 n :0an....

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

Comparison Test Consider a series that we are trying to determine convergence: Let’s say that all of the terms are positive: 0 a n . Then we if we can find a series 1 n n a that converges: Where 0 a b . This means that: 1 n n b n n 1 n n a must also converge: Why? If our series is stuck under a series for each term, then the partial sum is bounded for a n is bounded above for our artial sums for b his means that the limit cannot exceed the sum of the 1 n n a 1 n n b partial sums for b n . This means that the limit cannot exceed the sum of the series for b n (but since an are all positive, it is constantly increasing, so it will have to reach a bound and not shoot off to a negative infinity).

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

View Full Document
Comparison Test Consider a series that we are trying to determine divergence: Let’s say that all of the terms are positive: 0 a n . Then we if we can find a series 1 n n a that diverges: Where 0 b a . This means that: 1 n n b n n 1 n n a must also diverge: Why? If our series is stuck above a series for each term, then the partial sum is bounded for a n is bounded below by our partial ms for b his means if the sum of the es to infinity the sum of a ust 1 n n a 1 n n b sums for b n . This means if the sum of the b n goes to infinity, the sum of a n must be higher than that, which means it goes to infinity as well.
Strategy: Comparison Test etermine if the following series converges or diverges 3 n Determine if the following series converges or diverges To determine if the series converges or diverges using the comparison test, we need to

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.

{[ snackBarMessage ]}

### Page1 / 9

Lesson 20a - Comparison Test - ComparisonTest a n 1 n :0an....

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

View Full Document
Ask a homework question - tutors are online