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Few question related to power series

  1. Apr 18, 2010 #1
    1. The problem statement, all variables and given/known data

    let an= [tex]\sum^{k=1}_{n}[/tex] 1/[tex]\sqrt{k}[/tex]
    what is the radius of convergence of [tex]\Sigma[/tex][tex]\suma^{n=1}_{infinity} a_{n}x^n[/tex]


    i tired including the an term into the x^n equation then i got stuck.. help please



    2. Suppose that [tex]\alpha[/tex] and [tex]\beta[/tex] are positive real numbers with [tex]\alpha[/tex] < [tex]\beta[/tex]. find a power series with an interval of convergence that is of the given interval:

    I. ([tex]\alpha[/tex],[tex]\beta[/tex])
    II. [[tex]\alpha[/tex],[tex]\beta[/tex])

    i basically came up with power series that i know that has this convergence, but is there a systematic way of doing it, with a real proof.

    Thank you in advance
     
    Last edited: Apr 18, 2010
  2. jcsd
  3. Apr 18, 2010 #2

    lanedance

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    do you know about the harmonc series [tex] \sum \frac{1}{k}[/tex] and whether it converges?

    could you compare your seres to it?
     
  4. Apr 18, 2010 #3
    i don't think it would help much
     
  5. Apr 19, 2010 #4

    lanedance

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    ok but you know a_n diverges as n gets large right?

    have you tried a ratio test?
     
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