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Unit 10: Infinite Sequences and Series

AP Calculus BC — Note Packet

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Key Terms

Sequence

An ordered list of numbers, a parade of terms marching on ______.

Convergent Sequence

A sequence whose terms approach a finite number L as 'n' gets infinitely large. Its limit as n approaches infinity must be a ______ number.

Divergent Sequence

A sequence whose terms do not settle down to a specific finite value; its limit at infinity either doesn't exist or is ______.

Series

The sum of all the numbers in an infinite sequence, represented as an infinite ______.

nth Term Test for Divergence

If the limit as n approaches infinity of the individual terms (a_n) is NOT zero, then the series MUST ______.

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