Results 1 to 2 of 2

Thread: radius of convergence

  1. #1
    Feb 2009

    radius of convergence

    how come when u multiply a series by x^n or when u multiply a series by a constant, it doesnt change the radius of convergence? ex: the power series representation for e^x, the ROC doesnt change for the series represenation of x^2e^x, or if a constant was multiplied to the series represenation for e^x, i know that if u use the ratio test it's true that the ROC doesnt change, but like can someone explain to me like why intuitively it would be true?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Feb 2009
    What we're doing doing is a limit comparison to the geometric series.
    That's why we compare the next term to our present term.

    And since \biggl({x+1\over x}\biggr)^2\to 1 as x\to\infty

    theterms of the form x^2 can't change the interior of the interval of convergence.
    However, it can possibly alter convergence/divergence at the endpoints.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: March 27th 2011, 07:42 PM
  2. Replies: 1
    Last Post: May 13th 2010, 01:20 PM
  3. Replies: 2
    Last Post: May 1st 2010, 09:22 PM
  4. Replies: 1
    Last Post: November 13th 2009, 06:42 AM
  5. series convergence and radius of convergence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 15th 2008, 08:07 AM

Search Tags

/mathhelpforum @mathhelpforum