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Two Pwr Series Questions- relatively simple

  1. Feb 25, 2008 #1
    (at least I think they are simple !!)

    The 1st question is not a h/w problem. It is a question from textbook
    The 2nd question is a h/w problem.

    The series for log(1+x) is proven -1<x<=1. It then says the Taylor Series for (1/x)log(1+x) follows.
    Do they mean that the individual components of log(1+x) will be multiplied by (1/x). If true, would this apply for x, x^2 etc...

    Put e=exp(1). Use the Taylor Series expansion of exp to compute e.

    When I solve this, I can get the TS for exp. Do I have to evaluate it at x=1?


  2. jcsd
  3. Feb 25, 2008 #2


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    For the first one, if by components you mean power series terms, yes. For the second, yes, you have to put x=1 in. How many terms you need to keep depends on the accuracy of the answer you need. You'll need a taylor series remainder term if you need to be rigorous about it.
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