1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Homework Helper

    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


    User Avatar
    Homework Helper

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

    have you tried a ratio test?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Few question related to power series
  1. Power Series Question (Replies: 2)

  2. Power series question (Replies: 12)