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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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Section 8.4: Comparison Tests

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  1. Section 8.4: Comparison Tests

  2. Direct comparison test (Baby comparison test) Suppose 0 ≤ ak ≤ bk for all k

  3. Aside: To use any of the Comparison Tests, the terms must be positive.

  4. Diverges by the Direct Comparison Test.

  5. Converges by the Direct Comparison Test.

  6. Diverges by the Direct Comparison Test.

  7. But The baby test doesn’t really help much with

  8. Limit Comparison Test Suppose bk , ak > 0 and is not zero or infinity, then and either both converge or both diverge

  9. Looks like So and do the same thing The thing does is diverge! So diverges by the limit comparison test.

  10. Looks like So and do the same thing The thing does is converge ! So converges by the limit comparison test.

  11. Looks like So and do the same thing The thing does is diverge! So diverges by the limit comparison test.

  12. Looks like So and do the same thing The thing does is converge! So diverges by the limit comparison test.

  13. Zero Infinity test (Common Sense Comparison Test) Suppose bk, ak > 0 If and converges, then converges. If and diverges, then diverges.

  14. Compare with So is smaller than And Converges So Converges by the Zero-Infinity Test.

  15. Log-q Series converges if and only if q>1 (just like p-series)

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