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Testing Convergence (and Divergence)

Testing Convergence (and Divergence). A few major methods…. Integral Test: p-test Comparison Test Ratio Test Nth Root Test. …go to Maple worksheet. Integral Test. Applies to monotonic, positive, decreasing functions: Series converges if the integral does!. See 12.3 pg 765-66: #23, 24.

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Testing Convergence (and Divergence)

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  1. Testing Convergence(and Divergence)

  2. A few major methods… • Integral Test: • p-test • Comparison Test • Ratio Test • Nth Root Test …go to Maple worksheet

  3. Integral Test • Applies to monotonic, positive, decreasing functions: • Series converges if the integral does! See 12.3 pg 765-66: #23, 24

  4. Comparison Test • Sorta “common sense”: • “if series A converges and all of series B terms are less than or equal to series A terms then series B also converges” • The “catch” (there is always a catch!): the terms must be non-negative. • Example: Test convergence (or divergence) of: • A) • B) See 12.4

  5. Alternating Series • An alternating series looks like: • If the series converges • If the series converges absolutely

  6. Ratio and Root Tests • Consider the series • Let if: • r < 1 series converges • r > 1 series diverges • r = 1 ??????????? • Example:

  7. Ratio and Root Tests • Consider the series • Let if: • r < 1 series converges • r > 1 series diverges • r = 1 ??????????? • Example: See 12.6: 8, 30

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