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.

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

    Follow Math Help Forum on Facebook and Google+

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

    $\displaystyle -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 $\displaystyle r = 0.975^{1/n}$ 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 03:59 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, 10:59 AM
  2. Replies: 1
    Last Post: Aug 8th 2010, 11:29 AM
  3. Replies: 1
    Last Post: Feb 5th 2010, 03:33 AM
  4. Replies: 16
    Last Post: Nov 15th 2009, 04:18 PM
  5. Limit, Limit Superior, and Limit Inferior of a function
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: Sep 3rd 2009, 05:05 PM

Search Tags

/mathhelpforum @mathhelpforum