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Tests for Convergence, Pt. 1

Tests for Convergence, Pt. 1. The comparison test, the limit comparison test, and the integral test. In this presentation, we will base all our series at 1, but similar results apply if they start at 0 or elsewhere. Comparing series. . . Consider two series ,

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Section 8.4: Comparison Tests

Section 8.4: Comparison Tests. Direct comparison test ( Baby comparison test ) Suppose 0 ? a k ? b k for all k. Aside: To use any of the Comparison Tests, the terms must be positive. Diverges by the Direct Comparison Test. Converges by the Direct Comparison Test.

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Sect. 9-D Comparison Tests

Sect. 9-D Comparison Tests . The Direct comparison Test . If 0 < a n < b n for all n and positive terms, then: If the larger series converges, then the smaller series must also converge. If the smaller series diverges then the larger series must also diverge. The Direct comparison Test .

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Limit comparison - PowerPoint PPT Presentation

Tests for Convergence, Pt. 1

Section 8.4: Comparison Tests

Sect. 9-D Comparison Tests