ch11s1

# ch11s1 - 11.1 Sequences Sequence a list of numbers written...

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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: { } {} {} {} 123 11 ,,, nn n aaa a a a ∞∞ = K n Often an infinite sequence has a defining function. Some examples are shown below. 1 1 1 1 1 1 1, , , , , 234 sin sin 1,0, 1,0, ,sin , 22 n n a n a ππ  =   =− LL KK 2 n π All sequences do not have a defining function. It may difficult or impossible to given an explicit formula for the n th term in a sequence Example: (1) Sequence of prime integers. (2) The sequence whose th term is the th decimal digit of the number π. (3) Fibonacci sequence is defined recursively 12 1 1 1 3 1,1, 2, 3, 5, 8,13, 21, 34, 55, . .. n fff f f n −+ === + Sequences can be graphed on your calculator using the parametric mode. Example: Graph the sequence 1 1 n n + and then look at the terms of the sequence on your calculator.

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ch11s1 - 11.1 Sequences Sequence a list of numbers written...

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