Results 1 to 2 of 2

Thread: Limit

  1. #1
    Junior Member
    Jan 2009


    Hi, can someone evaluate this limit? I need it for a mathematical model, so, technically, I'm allowed to use technology (Mathematica gives the result as approximately 23.7), but if someone knows an easy way to solve this, it would be better.

    \lim_{n \to \infty} \frac{90n}{\displaystyle\sum_{i=0}^{4n} 0.975^ \frac{i}{n}}=?

    Follow Math Help Forum on Facebook and Google+

  2. #2
    May 2009
    I get the limit to be:

    -90 \frac{\ln 0.975}{1-0.975^4} = 23.6585 \dots

    The way I did this was to notice that the denominator is a geometric progression where r = 0.975^{1/n} and so use the formula for the sum of a geometric progression to re-express the denominator.

    Then, approaching the limit, the behaviour of the denominator is easy and the numerators' can be found by expanding in terms of a power series.

    It's as easy as that!
    Last edited by the_doc; May 16th 2009 at 04:59 PM. Reason: Corrected a missing negative sign!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 12
    Last Post: Aug 26th 2010, 11:59 AM
  2. Replies: 1
    Last Post: Aug 8th 2010, 12:29 PM
  3. Replies: 1
    Last Post: Feb 5th 2010, 04:33 AM
  4. Replies: 16
    Last Post: Nov 15th 2009, 05:18 PM
  5. Limit, Limit Superior, and Limit Inferior of a function
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: Sep 3rd 2009, 06:05 PM

Search Tags

/mathhelpforum @mathhelpforum