Results 1 to 2 of 2

Math Help - [SOLVED] riemann sum question

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    1

    [SOLVED] riemann sum question

    Hi, long-time lurker, first time poster

    The problem is this: find the limit of Sum[(i^2/(n^3 + i^3))] (going from i=1 to n) as n approaches infinity. Sorry I don't know how to write fancy math text but basically it's the limit of a series going to n as n --> infinity.

    I figure it's probably a riemann sum question, but I tend to have difficulty with those. Any help would be nice
    Last edited by mr fantastic; February 24th 2009 at 03:30 AM. Reason: Question deleted by OP has been restored.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    14
    \underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{i=1}^{n}{\frac{i^{2}}{n^{3}+i^{3}  }}=\underset{n\to \infty }{\mathop{\lim }}\,\frac{1}{n}\sum\limits_{i=1}^{n}{\left( \frac{i}{n} \right)^{2}\cdot \frac{1}{1+\left( \frac{i}{n} \right)^{3}}},

    thus \int_{0}^{1}{\frac{x^{2}}{1+x^{3}}\,dx} is the limit and the partition is \Delta x_{i}=\frac{1-0}{n}=\frac{1}{n}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Lower and Upper Riemann sums?
    Posted in the Calculus Forum
    Replies: 9
    Last Post: August 5th 2009, 07:50 AM
  2. [SOLVED] seemingly simple Riemann integral
    Posted in the Differential Geometry Forum
    Replies: 12
    Last Post: April 21st 2009, 03:07 PM
  3. [SOLVED] Another work as a Riemann sum problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 6th 2009, 12:18 PM
  4. [SOLVED] Riemann integrability
    Posted in the Calculus Forum
    Replies: 0
    Last Post: April 18th 2008, 12:54 PM
  5. [SOLVED] setting up riemann sums
    Posted in the Calculus Forum
    Replies: 0
    Last Post: February 26th 2008, 03:27 PM

Search Tags


/mathhelpforum @mathhelpforum