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Calculus II Chapter 8 Section 1&2 Sequences & Series

Calculus II Chapter 8 Section 1&2 Sequences & Series. David Dippel LoneStar-Montgomery. Sequence Definition and Notation. A Sequence is a function whose domain is the positive integers. We use subscript notation to denote terms of a sequence. Terms of a Sequence.

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Calculus II Chapter 8 Section 1&2 Sequences & Series

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  1. Calculus IIChapter 8 Section 1&2Sequences & Series David Dippel LoneStar-Montgomery

  2. Sequence Definition and Notation A Sequence is a function whose domain is the positive integers. We use subscript notation to denote terms of a sequence.

  3. Terms of a Sequence There are several ways to find terms of a sequence Recursively based on past terms In terms of n

  4. Limit of a Sequence A sequence that approaches a value is said to Converge. You can’t tell if a sequence converges just by looking at it.

  5. Adding terms of a Sequence =A Series

  6. Calculus IIChapter 8 Section 2Limits David Dippel LoneStar-Montgomery

  7. Limit of a Sequence Let L be a real number and let f be a function where If fn = an for each positive integer n, then This ties sequences to functions and we can then use what we have learned about limits of functions to find limits of sequences.

  8. Absolute Value Theorem This allows you to find limits when the signs change in a sequence.

  9. Show if the sequence has a limit and find the limit. The sequence is:

  10. Show if the sequence has a limit and find the limit. The sequence is: L’Hopital

  11. Show if the sequence has a limit and find the limit. The sequence is:

  12. Show if the sequence has a limit and find the limit. The sequence is:

  13. Monotonic Sequence A sequence with terms that are non-decreasing Or non-increasing

  14. Bounded Sequence A sequence is bounded above if there is a real number M such that A sequence is bounded below if there is a real number N such that

  15. Is the sequence monotonic and/or bounded? Monotonic No Upper Bound Lower Bound: (Since it is monotonic it starts at it’s lowest value)

  16. Graphing a sequence Select MODE, SEQ, and DOT Type in the function Under Window set the n values from 1 to 10 and the x & y max & min

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