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Warm Up

Warm Up. Tests for Convergence: The Integral and P-series Tests. The Integral Test. If f is positive, continuous, and decreasing for x > 1 and a n = f ( n ), then and Either both converge or diverge. Ex 1:. Ex 2:. The p-series test. The p-series Converges if p >1

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Warm Up

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  1. Warm Up

  2. Tests for Convergence:The Integral and P-series Tests

  3. The Integral Test If f is positive, continuous, and decreasing for x> 1 and an = f(n), then and Either both converge or diverge.

  4. Ex 1:

  5. Ex 2:

  6. The p-series test The p-series Converges if p >1 Diverges if 0 < p < 1 Test cannot be used if p < 0

  7. Ex 3: This is known as the HARMONIC series. The harmonic series DIVERGES.

  8. Ex 4:

  9. Ex 5:

  10. Ex 7:

  11. Ex 6:

  12. Mixed PracticeDetermine whether each series converges or diverges. If it converges and is possible to tell, determine what number it converges to. 1. 4. 2. 5. 3. 6.

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