Results 1 to 2 of 2

Math Help - Maclaurin Series, could you verify this?

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    19

    Maclaurin Series, could you verify this?

    Hi to you,

    Q: Find the Maclaurin series of f(x) = xe^x .
    Also find the associated radius of convergence.

    A: So far I have found this for the first part:
    f^n(x) = e^x(n+x).


    so it follows that:
    f^n(0) = n .


    and so:
    xe^x = \sum\frac{x^n}{(n-1)!} n going from 0 to infinity.

    That is:
    xe^x = x+x^2+\frac{x^3}{2!}+\frac{x^4}{3!}+....

    I am right for the first part?

    Second part:

    I did the ratio test and I got that the limit is smaller then 1.
    Therefore the sum is absolutely convergent...???

    Thanks in advance,
    Stev381



    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,105
    Thanks
    970
    Quote Originally Posted by Stev381 View Post
    Hi to you,

    Q: Find the Maclaurin series of f(x) = xe^x .
    Also find the associated radius of convergence.

    A: So far I have found this for the first part:
    f^n(x) = e^x(n+x).


    so it follows that:
    f^n(0) = n .


    and so:
    xe^x = \sum\frac{x^n}{(n-1)!} n going from 0 to infinity. n = 1 to infinity

    That is:
    xe^x = x+x^2+\frac{x^3}{2!}+\frac{x^4}{3!}+.... fine

    I am right for the first part?

    Second part:

    I did the ratio test and I got that the limit is smaller then 1. yes, 0 is < 1
    Therefore the sum is absolutely convergent...??? correct

    ...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: January 26th 2010, 09:06 AM
  2. Replies: 2
    Last Post: September 16th 2009, 08:56 AM
  3. Binomial Series to find a Maclaurin Series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 21st 2009, 08:15 AM
  4. Multiplying power series - Maclaurin series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 8th 2009, 12:24 AM
  5. Replies: 1
    Last Post: May 5th 2008, 10:44 PM

Search Tags


/mathhelpforum @mathhelpforum