calc test 1 - Indeterminate form Powers Geometric Series*r is the ratio between terms Is convergent if |r| 1 Is divergent if |r| 1 Integral Text Suppose

# calc test 1 - Indeterminate form Powers Geometric Series*r...

• Notes
• 2

This preview shows page 1 - 2 out of 2 pages.

Indeterminate form, Powers : Geometric Series : *r is the ratio Is convergent if |r| 1 between terms Is divergent if |r| 1 Integral Text: Suppose f is a continuous, positive, decreasing function on [1, ) and let A = f(n). Then the series A is convergent if and only if the improper integral f(x) dx is convergent. In other words: 1. f(x) dx is convergent, then A is convergent. 2. f(x) dx is divergent, then A is divergent P-series test : The P-series is convergent if p 1 and divergent if p 1. Comparison Test : Suppose that A and B are series with positive terms. 1. If B is convergent and A B for all n, the A is also convergent. 2. If B is divergent and A B for all n, then A is also divergent. Limit Comparison Test : Suppose that