Results 1 to 4 of 4
Like Tree3Thanks
  • 1 Post By SlipEternal
  • 1 Post By HallsofIvy
  • 1 Post By SlipEternal

Math Help - Root Test for series

  1. #1
    Newbie
    Joined
    Nov 2013
    From
    ireland
    Posts
    7

    Root Test for series

    Using the root test or otherwise, determine whether the given series
    converges or diverges.


    A) ∑ (n^2+1/2n^2+n)^n

    n=1

    ∞B) ∑ (1-2/n)^n^2

    n=1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,758
    Thanks
    676

    Re: Root Test for series

    I can't read your post. What is in the numerator, what is in the denominator, what is being taken to the n-th power? Use more parentheses.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,298
    Thanks
    1275

    Re: Root Test for series

    Quote Originally Posted by Dfaulk044 View Post
    Using the root test or otherwise, determine whether the given series
    converges or diverges.


    A) ∑ (n^2+1/2n^2+n)^n
    I think you mean \sum_{n=1}^\infty \left(\frac{n^2+ 1}{2n^2+ n}\right)^n
    (what you wrote was a sum of n^2+ (1/n^2)+n)
    Since you mention the root test, the nth root of each term is \frac{n^2+ 1}{2n^2+ n}. What is the limit of that as n goes to infinity? What does that tell you about the sum?

    n=1

    ∞B) ∑ (1-2/n)^n^2

    n=1
    Here, I assume you mean \sum_{n= 1}^\infty \left(1- \frac{2}{n}\right)^{n^2}
    The nth root of that is \left(1- \frac{2}{n}\right)^n. What is the limit of that? (You really need to know that \lim_{n\to\infty}\left(1+ \frac{1}{n}\right)^n= e.)
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,758
    Thanks
    676

    Re: Root Test for series

    Also helpful is the fact that \lim_{n \to \infty} \left( 1 + \dfrac{x}{n} \right)^n = e^x.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Root Test to an Infinite Series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 15th 2012, 06:06 PM
  2. Replies: 5
    Last Post: April 7th 2011, 04:44 AM
  3. Series (ratio and root test)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 5th 2010, 06:48 AM
  4. Replies: 7
    Last Post: June 4th 2009, 09:33 PM
  5. series convergence by root test
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 7th 2009, 04:33 PM

Search Tags


/mathhelpforum @mathhelpforum