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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 < 1. By comparison test, our original series must also converge. | an | Ln For L > 1, the proof is identical except we have , but the series nk
on the right is divergent (geometric series L > 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:
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:
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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.
- Summer '00
- Calculus, Lecture Notes, MATH1004, Kyle Harvey