Results 1 to 8 of 8

Math Help - Converge or Diverge?

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    225

    Converge or Diverge?

    An = n^3 / (n + 5)

    Can I just take the limit and say this is equal to 1 / 0 so it diverges?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by veronicak5678 View Post
    An = n^3 / (n + 5)

    Can I just take the limit and say this is equal to 1 / 0 so it diverges?
    It diverges because this is equivalent to

    \frac{n+125-125}{n+5}=\frac{n^3+125}-\frac{125}{n+5}=n^2+5n+25-\frac{125}{n+5}

    Now what is the limit of that as it goes to infinity?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Aug 2008
    Posts
    225
    1 + 0 + 0 - 125/5 = -24 ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jun 2008
    Posts
    792
    What are you on about? You're subbing 1 here and 0 there. Take the limit as n goes to infinity
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    Quote Originally Posted by Mathstud28 View Post
    It diverges because this is equivalent to

    \frac{n+125-125}{n+5}=\frac{n^3+125}-\frac{125}{n+5}=n^2+5n+25-\frac{125}{n+5}

    Now what is the limit of that as it goes to infinity?
    While that's true, isn't is much easier to simply take the original form of A_n and easily see that the limit is infinity as n approaches infinity?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Aug 2008
    Posts
    225
    I think that's more along the lines of what I was supposed to be doing, anyway...

    So I'll just take the limit off the bat and say it diverges.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by veronicak5678 View Post
    An = n^3 / (n + 5)

    Can I just take the limit and say this is equal to 1 / 0 so it diverges?
     \frac{n^3}{n+5} \geq \frac{n^3}{n+5n}=\tfrac{1}{6}n^2 and \lim ~ \tfrac{1}{6}n^2 = \infty
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    Aug 2008
    Posts
    225
    Got it. Thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Converge or diverge
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 15th 2010, 08:58 PM
  2. Converge or Diverge?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 15th 2010, 08:39 AM
  3. Converge or diverge?
    Posted in the Calculus Forum
    Replies: 6
    Last Post: November 22nd 2009, 08:54 PM
  4. Converge/Diverge help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 9th 2009, 11:57 AM
  5. Diverge/Converge
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 14th 2008, 01:55 PM

Search Tags


/mathhelpforum @mathhelpforum