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Unit 12

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Unit 12: Sequences and Series

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Vocabulary

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Arithmetic Sequences

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Geometric Sequences

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Unit 12: Sequences and Series

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Series

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Sigma Notation

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Series Shortcuts

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Unit 12: Sequences and Series

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Informal Definition of a Limit Let f be a function and c be a real number such that f(x) is defined for all values of x near x=c. Whenever x takes on values closer and closer but not equal to c (on both sides of c), the corresponding values of f(x) get very close to, and possibly equal, to the same real number L and the values of f(x) can be made arbitrarily close to L by taking values of x close enough to c, but not equal to c.

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Definition of a Limit

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Examples 3

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∞

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When Limits Do Not Exist Does Not Exist

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When Limits Do Not Exist Does Not Exist

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When Limits Do Not Exist Does Not Exist

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Limits at Infinity

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Examples 6 1

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0 0

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Unit 12: Sequences and Series

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Convergence of a Sequence

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Convergence of a Series

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Aim: What is the arithmetic series ? Do Now: Find the sum of each of the following sequences: a) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 b) 1 + 2 +

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