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Radius of convergence

  1. Mar 19, 2009 #1
    Having a hard time with this one: E 1/n^x , have tried too use n^-x=e^(-x ln n) which in turn e^(...) = lim n->OO (1-(x ln n)/n)^n and then go on with finding the centre, but I feel I'm far far off. How to get it like E an(x-c)^n and use the more straight foreward path.
  2. jcsd
  3. Mar 19, 2009 #2
    Hi incus!

    The series


    is not a power series, so it does not have a radius convergence. It does however have a region of convergence (the x so that the series converges). Is x supposed to be a real or complex variable?

    In the case where x is a real variable you can use the integral test to find the region of convergence.

    The case where x is complex can be reduced to the real case by considering the real part of x and the absolute value of the terms in the series.
  4. Mar 19, 2009 #3


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    You can't ask for a radius of convergence unless you say which point you are expanding around. I'm guessing the actual question is 'for what values of x does the series converge'. Is x complex? Hint: your series is a p-series. And your series defines part of the Riemann zeta function.
  5. Mar 20, 2009 #4
    Thanks for steering me in the right direction yyat and Dick. Got blinded by the question.
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