Results 1 to 6 of 6

Math Help - Does this sequence converge or diverge?

  1. #1
    Member
    Joined
    Sep 2010
    Posts
    151
    Thanks
    3

    Does this sequence converge or diverge?

    f= (-1)^n \frac{n}{n+1}

    If it converges find the limit and if it diverges justify why.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,540
    Thanks
    780

    Re: Does this sequence converge or diverge?

    I recommend calculating the first several elements and making a conjecture.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,589
    Thanks
    1445

    Re: Does this sequence converge or diverge?

    It definitely does not converge. \displaystyle \begin{align*} \frac{n}{n + 1} \to 1 \end{align*} as \displaystyle \begin{align*} n \to \infty \end{align*}, so eventually the terms will oscillate between -1 and 1.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2012
    From
    United States
    Posts
    11

    Re: Does this sequence converge or diverge?

    Does this help you?

    \lim_{n\to\infty}(-1)^n\frac{n}{n+1}

    \rightarrow \lim_{n\to\infty}(-1)^n\frac{n/n}{n/n+1/n}

    \rightarrow \lim_{n\to\infty}(-1)^n\frac{1}{1+0}

    \rightarrow \lim_{n\to\infty}(-1)^n(1)
    Last edited by amillionwinters; September 10th 2012 at 06:01 AM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Sep 2010
    Posts
    151
    Thanks
    3

    Re: Does this sequence converge or diverge?

    Thanks for the replies. I understand the sequence definitely diverges.

    Please note my brother asked me this question and it is not part of my coursework(and i have never done anything like this before), which is why i didn't make an attempt at a solution, however i am still interested in the answer.

    His question asked to find an appropriate epsilon and n to justify why the series diverges.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,708
    Thanks
    1638
    Awards
    1

    Re: Does this sequence converge or diverge?

    Quote Originally Posted by linalg123 View Post
    Please note my brother asked me this question and it is not part of my coursework(and i have never done anything like this before), which is why i didn't make an attempt at a solution, however i am still interested in the answer.
    His question asked to find an appropriate epsilon and n to justify why the series diverges.
    If f_n=\frac{(-1)^nn}{n+1} and n>1 then it can be shown that f_n>\tfrac{1}{2} if n even and f_n<-\tfrac{1}{2} if n is odd.

    That means |f_{n+1}-f_n|>1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: March 25th 2011, 01:21 AM
  2. Sequence - Converge or Diverge?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 16th 2010, 10:57 PM
  3. converge or diverge?
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: October 10th 2009, 07:51 PM
  4. sequence converge or diverge
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 6th 2009, 11:25 PM
  5. Sequence converge or diverge?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 9th 2008, 11:03 AM

Search Tags


/mathhelpforum @mathhelpforum