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Math Help - Power Series

  1. #1
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    Power Series

    This is number 4 of the set of real analysis questions:

    If we have:
     \sum_{n=0}^{\infty} a_n*x^n =  \sum_{n=0}^{\infty} b_n*x^n
    for all x in an interval (-R,R), prove that a_n = b_n for all n = 0,1,2...
    (Start by showing that a_0 = b_0.)
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  2. #2
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    Quote Originally Posted by ajj86 View Post
    This is number 4 of the set of real analysis questions:

    If we have:
     \sum_{n=0}^{\infty} a_n*x^n =  \sum_{n=0}^{\infty} b_n*x^n
    for all x in an interval (-R,R), prove that a_n = b_n for all n = 0,1,2...
    (Start by showing that a_0 = b_0.)
    If ture for all x then certain true for x = 0 and after substituting this all the terms dissappear except a_0 = b_0

     \sum_{n=1}^{\infty} a_n x^n = \sum_{n=1}^{\infty} b_n x^n

    Then, cancel and x and repeat.
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