Results 1 to 2 of 2

Math Help - can't figure out infinite sum of integral, halfway there

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    york
    Posts
    7

    can't figure out infinite sum of integral, halfway there

    Hi!
    please could someone point out where i went wrong. the question is attached (sorry for the lack of latex)
    i need to find

    lim(as a tends to inf) of SUM (from n=1 to inf) of INTEGRAL (from 1 to inf) of the function exp(-2nx)*(1+ x/a)^(an) dx

    so far i took the limit inside the bracket to get
    lim (1+x/a)^na = e^(xn)
    then you get
    SUM [ INTEGRAL (exp(-2nx)*exp(nx)) dx]
    = SUM [INTEGRAL exp(-nx) dx]
    = SUM [ -1/n *exp(-xn) ] from 1 to inf
    = SUM [ -1/n *exp (-n) - 0]

    and that sum is pretty funky, i don't know how to arrive at the given result
    Attached Thumbnails Attached Thumbnails can't figure out infinite sum of integral, halfway there-capture.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,668
    Thanks
    608

    Re: can't figure out infinite sum of integral, halfway there

    Hey cassius2020.

    Hint: try looking at the Taylor series for the logarithmic function:

    Taylor Series Expansions of Logarimathic Functions
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Halfway through equation
    Posted in the Algebra Forum
    Replies: 7
    Last Post: January 7th 2010, 02:05 PM
  2. Physics 11 Questions - Halfway Solved
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: November 10th 2009, 01:33 PM
  3. Replies: 2
    Last Post: September 5th 2009, 03:24 PM
  4. [SOLVED] Halfway Between Fraction
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 11th 2009, 12:51 AM
  5. I cant figure out this Indefinite integral ..
    Posted in the Calculus Forum
    Replies: 6
    Last Post: April 1st 2007, 04:03 PM

Search Tags


/mathhelpforum @mathhelpforum