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Sec 11.1: SEQUENCES DEF: A sequence is a list of numbers written in a definite order: Example first term second term n-th term Example Example
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Sec 11.1: SEQUENCES DEF: A sequence is a list of numbers written in a definite order: Example Example Example Find a formula for the general term of the sequence
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Sec 11.1: SEQUENCES Example Example Example
Find a formula for the general term of the sequence Example Find a formula for the general term of the sequence the digit in the th decimal place of the number pi Example Find a formula for the general term of the sequence This sequence arose when the 13th-century Italian mathematician known as Fibonacci
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Sec 11.1: SEQUENCES PLOT THE SEQUENCES Example
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Sec 11.1: SEQUENCES LIMIT OF THE SEQUENCES Example Example
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Sec 11.1: SEQUENCES
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Sec 11.1: SEQUENCES
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Sec 11.1: SEQUENCES Example Note:
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Sec 11.1: SEQUENCES Example
Determine whether the sequence is convergent or divergent.
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continuous convergent convergent Sec 11.1: SEQUENCES THEOREM; Example
Find
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Sec 11.1: SEQUENCES THEOREM; Example Find where
(SQUEEZE THEOREM FOR SEQUENCES) Example Find where
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Sec 11.1: SEQUENCES Example
For what values of r is the sequence convergent?
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Sec 11.1: SEQUENCES
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Sec 11.1: SEQUENCES DEFINITION increasing DEFINITION decreasing
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if it is either increasing or decreasing.
Sec 11.1: SEQUENCES DEFINITION increasing DEFINITION decreasing DEFINITION monotonic if it is either increasing or decreasing.
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Sequences (up to page 682 only, End of example 12)
Sec 11.1: SEQUENCES DEFINITION increasing decreasing DEFINITION Example Is the sequence increasing or decreasing Example12 Is the sequence increasing or decreasing 2-solutions SYLLABUS Sequences (up to page 682 only, End of example 12)
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How to find a limit of a sequence
Sec 11.1: SEQUENCES How to find a limit of a sequence THEOREM; continuous convergent convergent THEOREM; (SQUEEZE THEOREM) THEOREM; Every bounded, monotonic sequence is convergent
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How to find a limit of a sequence
Sec 11.1: SEQUENCES How to find a limit of a sequence (IF you can) Convert into function and use Math-101 to find the limit. Use other prop. To find the limit squeeze Example: Example:
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Sec 11.1: SEQUENCES
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Sec 11.1: SEQUENCES
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Sec 11.1: SEQUENCES
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Sec 11.1: SEQUENCES
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Sec 11.1: SEQUENCES
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Sec 11.1: SEQUENCES
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Sec 11.1: SEQUENCES
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if there is a number M such that
Sec 11.1: SEQUENCES DEFINITION bounded above if there is a number M such that Example Is the sequence bounded above or below DEFINITION bounded below if there is a number m such that
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If it is bounded above and below
Sec 11.1: SEQUENCES DEFINITION bounded above DEFINITION bounded below DEFINITION bounded If it is bounded above and below Example Is the sequence bounded
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Sec 11.1: SEQUENCES THEOREM; increasing bounded above convergent
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Every bounded, monotonic sequence is convergent
Sec 11.1: SEQUENCES THEOREM; increasing bounded above convergent THEOREM; decreasing bounded below convergent THEOREM; Every bounded, monotonic sequence is convergent NOTE: The theorem doesn’t tell us what the value of the limit is.
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Sec 11.1: SEQUENCES
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Sec 11.1: SEQUENCES TERM-082
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Sec 11.1: SEQUENCES TERM-082
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Sec 11.1: SEQUENCES TERM-092
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Sec 11.1: SEQUENCES TERM-092
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