Results 1 to 4 of 4

Math Help - 2 more questions

  1. #1
    Member tinspire's Avatar
    Joined
    Jul 2014
    From
    cali
    Posts
    113
    Thanks
    17

    2 more questions

    these are the last two questions that i'll have for the rest of the semester (i hope)

    find the taylor series for $f(x)=x^4-3x^2+1$ centered at the given value of $a=1$. assume that $f$ has a power series expansion. also find the associated radius of convergence.


    find the sum of the series $\sum_{n=0}^{\infty} \frac{2^n}{3^nn!}$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member tinspire's Avatar
    Joined
    Jul 2014
    From
    cali
    Posts
    113
    Thanks
    17

    Re: 2 more questions

    i know how to do the first one the way where you make a table but is there any other way to do it?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,771
    Thanks
    1140

    Re: 2 more questions

    Quote Originally Posted by tinspire View Post
    i know how to do the first one the way where you make a table but is there any other way to do it?
    I assume you mean a table of derivatives evaluated at $a$. For a general polynomial like this any way you come up with is going to boil down to evaluating $f^{(k)}(a)$.


    For the 2nd problem you should know that

    $e^x = \displaystyle{\sum_{n=0}^\infty}\dfrac{x^n}{n!}$

    Thus

    $\displaystyle{\sum_{n=0}^\infty}\dfrac{2^n}{3^n n!}=\displaystyle{\sum_{n=0}^\infty}\dfrac{(2/3)^n}{n!}=e^{2/3}$
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member tinspire's Avatar
    Joined
    Jul 2014
    From
    cali
    Posts
    113
    Thanks
    17

    Re: 2 more questions

    i figured them out. thanks though. i just remembered that $e^x$ is equal to that.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help with a few questions.
    Posted in the Statistics Forum
    Replies: 22
    Last Post: February 24th 2013, 09:43 PM
  2. Replies: 1
    Last Post: November 1st 2012, 06:30 AM
  3. Replies: 4
    Last Post: July 19th 2008, 08:18 PM
  4. Some questions!
    Posted in the Algebra Forum
    Replies: 5
    Last Post: September 5th 2007, 02:04 PM
  5. Replies: 3
    Last Post: August 1st 2005, 02:53 AM

Search Tags


/mathhelpforum @mathhelpforum