Results 1 to 3 of 3

Math Help - 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 sqrt(n + 1) goes to infinity and 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 lim| sqrt(n + 1) - sqrt(n) | = 0.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,673
    Thanks
    1618
    Awards
    1
    \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: February 4th 2011, 02:33 AM
  2. Replies: 6
    Last Post: August 13th 2010, 01:03 AM
  3. Replies: 1
    Last Post: August 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: September 3rd 2009, 05:05 PM
  5. limit problem
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: August 20th 2009, 10:37 AM

Search Tags


/mathhelpforum @mathhelpforum