11.1.13-eg-1 - -1 n =-1 n odd 1 n even or-1 n 1 = 1 n odd-1 n even(equivalently-1 n-1 may be used in place of the latter In this particular example

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Example Consider the following sequence: - 2 1 , 4 2 , - 8 3 , 16 4 , .... Write a formula for the nth term a n in this sequence. Solution: The general terms of a sequence are expressed as a 1 , a 2 , a 3 , a 4 , ..., so it must be in this case that a 1 = - 2 1 = - 2 1 1 , a 2 = 4 2 = 2 2 2 , a 3 = - 8 3 = - 2 3 3 , a 4 = 16 4 = 2 4 4 , and so on. Thus the nth term may be written a n = ± 2 n n , where it remains to determine the precise sign of a n as a function of n . The usual way to represent an alternating sign in a sequence is via the use of
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Unformatted text preview: (-1) n = (-1 , n odd , 1 , n even , or (-1) n +1 = ( 1 , n odd ,-1 , n even , (equivalently (-1) n-1 may be used in place of the latter). In this particular example, the sequence is negative for odd values of n and positive for even values of n , so we can write the nth term as a n = (-1) n 2 n n ....
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This note was uploaded on 04/02/2012 for the course MTH 132 taught by Professor Kihyunhyun during the Fall '10 term at Michigan State University.

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