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chap11sec1

chap11sec1 - 11.1 Sequences ..Aninfinitesequence...

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11.1 Sequences Sequence – a list of numbers written in a definite order.  We will only be concerned with  infinite sequences. An infinite sequence  of real numbers is an ordered, unending list. Some notation for infinite sequences: { } { } { } { } 1 2 3 1 1 , , , n n n n a a a a a a = K Often an infinite sequence has a defining function. Some examples are shown below. 1 1 1 1 1 1 1 1 1, , , , , 2 3 4 sin sin 1,0, 1,0, ,sin , 2 2 2 n n a n n n n n n a π π π = = - L L K K All sequences do not have a defining function.  It may difficult or impossible to given an explicit formula for the nth term in a  sequence  Example: (1) Sequence of prime integers. (2) The sequence whose nth term is the nth decimal digit of the number  π. (3) Fibonacci sequence is defined recursively 1 2 1 1 1, 1 3 1,1,2,3,5,8,13,21,34,55,... n n n f f f f f n - + = = = + Sequences can be graphed on your calculator using the parametric mode.

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chap11sec1 - 11.1 Sequences ..Aninfinitesequence...

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