Results 1 to 3 of 3

Thread: Limit problem

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    8

    Limit problem

    I am struggling to write a formal proof for the following problem. I know that you can multiply by the conjugate and the get the sum of the two square roots over the quantity one. Then $\displaystyle sqrt(n + 1)$ goes to infinity and $\displaystyle sqrt(n)$ also goes to infinity, thus the sum goes to infinity. If the whole denominator goes to infinity, then one over the denominator goes to zero.

    However, I don't know if that is a sufficient proof. I would appreciate any further insight anyone can offer. Thank you in advance.

    Problem:
    Show that $\displaystyle lim| sqrt(n + 1) - sqrt(n) | = 0$.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,800
    Thanks
    2829
    Awards
    1
    $\displaystyle \sqrt {n + 1} - \sqrt n = \frac{1}{{\sqrt {n + 1} + \sqrt n }} \leqslant \frac{1}{{\sqrt n }}$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    8
    Ah. Right. That's it. Thank you very much. Very helpful!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Limit problem
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: Feb 4th 2011, 02:33 AM
  2. Replies: 6
    Last Post: Aug 13th 2010, 01:03 AM
  3. Replies: 1
    Last Post: Aug 8th 2010, 11:29 AM
  4. 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
  5. limit problem
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Aug 20th 2009, 10:37 AM

Search Tags


/mathhelpforum @mathhelpforum