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Section 1: Sequences & Series https://sites.google.com/site/bchsapcalculusbc /units/unit-10-chp-11-sequences-series https://sites.google.com/site/bchsapcalculusbc /units/unit-10-chp-11-sequences-series
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Sequence: Sequence: a function whose domain is the non-negative integers. a n = terms in the sequence n = 1, 2, 3 … or 0, 1, 2…
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n factorial = n! The product of the first n natural numbers. The product of the first n natural numbers.
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Ex 1: Find the first 5 terms: a) b)
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Give an expression for the general form of the sequence: Give an expression for the general form of the sequence: Ex 2:
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Limits of Sequences If the limit,, exists then {a n } converges. If the limit DNE, then {a n } diverges.
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Ex 3: Does the following sequence Converge OR Diverge?
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Series or Infinite Series: Series or Infinite Series: the sum of the terms of an infinite sequence.
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Partial Sums: Partial Sums:
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Find the 5 th, 10 th, and 25 th partial sum of the series: Find the 5 th, 10 th, and 25 th partial sum of the series: Ex 4:
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Limits of Series If the sequence S n diverges, then a n is a divergent series.
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If the sequence S n converges to a value S, then a n is a convergent series such that: If S exists, then S is the sum of the infinite series.
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Properties of Sums Properties of Sums 1) 1)
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Properties of Sums Properties of Sums 2) 2)
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If then the series is DIVERGENT. The nth Term Test:
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Show that the following series diverges Show that the following series diverges Ex 5:
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Harmonic Series DIVERGENT!
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Section 1A WS #1 – 6 all, # 7 – 15 odds
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Geometric Series a = 1 st term r = common ratio
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Sum of an Infinite Geometric Series: Sum of an Infinite Geometric Series: If |r| < 1
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The Geometric Series Test:
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Convergent? If so, find the sum: Convergent? If so, find the sum: a) c) b) d) Ex 6:
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Write 0.8888888… as a fraction. Write 0.8888888… as a fraction. Ex 7:
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Ex 8: Does the following series Converge OR Diverge?
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Section 1B WS #17 – 25 odds, 27 – 37 odds, 40 – 44 all
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Ex 9: Does the following sequence Converge OR Diverge?
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