Results 1 to 2 of 2

Math Help - Maclaurin Series Problem Correct?

  1. #1
    Newbie
    Joined
    Jan 2013
    From
    United States
    Posts
    10

    Maclaurin Series Problem Correct?

    Riemann sum of n = 0 to infinity, (-1)^n * x^(2n) / n! for all real x, then f''(0) = ?

    I changed this to (-x^2)^n / n! in order to make it similar to the e^x maclaurin series. I then used e^(-x^2) as my function for the series and took the second derivative which I got to be -2 + 6x^2 - 5x^4 +... I plugged in 0 for x and thus the answer is -2. Is this logic correct?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Maclaurin Series Problem Correct?

    Quote Originally Posted by achiu17 View Post
    Riemann sum of n = 0 to infinity, (-1)^n * x^(2n) / n! for all real x, then f''(0) = ?

    I changed this to (-x^2)^n / n! in order to make it similar to the e^x maclaurin series. I then used e^(-x^2) as my function for the series and took the second derivative which I got to be -2 + 6x^2 - 5x^4 +... I plugged in 0 for x and thus the answer is -2. Is this logic correct?
    In my opinion your solution is correct. I've used an other method:

    The Maclaurin serie of a function f(x) is given by
    f(x)= \sum_{n=0}^{\infty} \frac{f^{(n)}(0)}{n!}x^n = f(0)+f'(0)x+\frac{x^2}{2}f''(0)+\ldots

    In this case we have the following sum
    \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{n!} = 1 - x^{2}+\frac{x^4}2}+\ldots

    If we compare both series the we notice that \frac{f''(0)}{2} = -1 \Rightarrow f''(0)=-2
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. maclaurin series problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 8th 2010, 04:18 PM
  2. Maclaurin series problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 28th 2009, 11:58 PM
  3. Maclaurin Series Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 27th 2009, 09:30 PM
  4. MacLAurin Series problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 26th 2009, 11:10 PM
  5. Maclaurin Series Problem
    Posted in the Calculus Forum
    Replies: 7
    Last Post: April 20th 2008, 05:36 PM

Search Tags


/mathhelpforum @mathhelpforum