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Math Help - power series

  1. #1
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    power series

    i having great problems trying to find the R= radius of convergence.

    the qns is. show that R= infinity for the series exp(x) = 1+ x/1! + x^2 /2! +...

    my working:

    exp (x) = summation from n=0 to infinity (x^n)/n!

    i cant think of a way how to make n start from 1 instead of 0.

    so in this case, let a_n = 1/n!

    then using ratio test, R = lim (a_n+1 / a_n) = 1/(n+1)

    thus as n tends to infinity, R tends to 0... but i need to show that R= infinity
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  2. #2
    Senior Member Dinkydoe's Avatar
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    http://en.wikipedia.org/wiki/Radius_of_convergence

    eh no.... R=\lim_{n\to\infty}|(a_n/a_{n+1})|= \lim_{n\to\infty}(n+1)=\infty
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  3. #3
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    are you sure?
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  4. #4
    Senior Member Dinkydoe's Avatar
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    Quote Originally Posted by alexandrabel90 View Post
    are you sure?
    Have you checked the link?

    Radius of convergence - Wikipedia, the free encyclopedia

    See definition of Radius of convergence.
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  5. #5
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    oh! becos my lecture notes wrote it the other way round. guess its a mistake in the notes.

    thanks for pointing it out to me
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  6. #6
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    The root test gives \left( {\forall x} \right)\left[ {\dfrac{{\left| x \right|}}{{\sqrt[n]{{n!}}}} \to 0} \right].

    Because it converges for all x, what is the radius of convergence?
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  7. #7
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    infinity(:
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