series-strategies

# series-strategies - Instructor: Dr. Farzana Chaudhry MATH...

This preview shows pages 1–2. Sign up to view the full content.

Instructor: Dr. Farzana Chaudhry MATH 1042 -Calculus II CH 8. Strategy for Series . Here is a quick listing of all the test that we’ve got. 1. Divergence Test: If lim n →∞ a n ± = 0 then a n will diverge. 2. Integral Test: Suppose that f ( x ) is a positive, decreasing function on the interval [ k, ) and that f ( n ) = a n then, i. If R k f ( x ) dx is convergent so is X n = k a n . ii. If R k f ( x ) dx is divergent so is X n = k a n . 3. Comparison Test: Suppose that we have two series a n and b n with a n 0 and b 0 for all n and a n b n for all n . Then, i. If b n is convergent then so is a n . ii. If b n is divergent then so is a n . 4. Limit Comparison Test: Suppose that we have two series a n and b n with a n 0 and b n ) for all n . Suppose that lim n →∞ a n b n = L i. If L is positive (i.e. L > 0 ) and is ﬁnite (i.e. L < ) then either both series converge or both series diverge. ii.

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.

## This note was uploaded on 04/18/2008 for the course MATH 1042 taught by Professor Dr.z during the Spring '08 term at Temple.

### Page1 / 2

series-strategies - Instructor: Dr. Farzana Chaudhry MATH...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online