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Sequence : a function whose domain is the non-negative integers.

Section 1 : Sequences & Series https://sites.google.com/site/bchsapcalculusbc/units/unit-10-chp-11-sequences-series. Sequence : a function whose domain is the non-negative integers. a n = terms in the sequence n = 1, 2, 3 … or 0, 1, 2…. n factorial = n!.

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Sequence : a function whose domain is the non-negative integers.

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  1. Section 1: Sequences & Serieshttps://sites.google.com/site/bchsapcalculusbc/units/unit-10-chp-11-sequences-series

  2. Sequence: a function whose domain is the non-negative integers. • an = terms in the sequence • n = 1, 2, 3 … or 0, 1, 2…

  3. n factorial = n! • The product of the first n natural numbers.

  4. Ex 1: Find the first 5 terms:a)b)

  5. Ex 2: • Give an expression for the general form of the sequence:

  6. Limits of Sequences • If the limit, , exists then {an} converges. • If the limit DNE, then {an} diverges.

  7. Ex 3: Does the following sequence Converge OR Diverge?

  8. Series or Infinite Series: the sum of the terms of an infinite sequence.

  9. Partial Sums:

  10. Ex 4: • Find the 5th, 10th, and 25th partial sum of the series:

  11. Limits of Series • If the sequence Sn diverges, then  an is a divergent series.

  12. If the sequence Sn converges to a value S, then  an is a convergent series such that: If S exists, then S is the sum of the infinite series.

  13. Properties of Sums

  14. Properties of Sums

  15. The nth Term Test: If then the series is DIVERGENT.

  16. Ex 5: • Show that the following series diverges

  17. Harmonic Series • DIVERGENT!

  18. Section 1A WS#1 – 6 all,# 7 – 15 odds

  19. Geometric Series • a = 1st term • r = common ratio

  20. Sum of an Infinite Geometric Series: If |r| < 1

  21. The Geometric Series Test:

  22. Ex 6: • Convergent? If so, find the sum: • c) • d)

  23. Ex 7: • Write 0.8888888… as a fraction.

  24. Ex 8: Does the following series Converge OR Diverge?

  25. Section 1B WS#17 – 25 odds,27 – 37 odds,40 – 44 all

  26. Ex 9: Does the following sequence Converge OR Diverge?

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