Results 1 to 4 of 4
Like Tree3Thanks
  • 1 Post By zzephod
  • 1 Post By zzephod
  • 1 Post By Plato

Math Help - Series

  1. #1
    csc
    csc is offline
    Newbie
    Joined
    Feb 2014
    From
    brunei
    Posts
    6

    Series

    Series-1.png

    Hi, I couldnt do these 3 questions. Anyone can help which method to use please?

    I tried divergence test for d. but I got 0 which means divergence test failed. and....

    h) I used l'ho and got 1. is that correct?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Apr 2012
    From
    Erewhon
    Posts
    180
    Thanks
    119

    Re: Series

    The first is a series with $$a_n=-\frac{1}{n(n+1)}$$ here $|a_n|<1/(n+1)^2$ and since $\sum_{i=2}^{\infty}1/n^2$ converges the series here converges absolutely and so converges by the comparison test.

    .
    Thanks from csc
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Apr 2012
    From
    Erewhon
    Posts
    180
    Thanks
    119

    Re: Series

    Quote Originally Posted by csc View Post
    Click image for larger version. 

Name:	1.png 
Views:	16 
Size:	9.7 KB 
ID:	30530

    Hi, I couldnt do these 3 questions. Anyone can help which method to use please?

    I tried divergence test for d. but I got 0 which means divergence test failed. and....

    h) I used l'ho and got 1. is that correct?
    For the second two you should note that $\lim_{n \to \infty} a_n =1$ so they do not converge.

    .
    Thanks from csc
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,659
    Thanks
    1616
    Awards
    1

    Re: Series

    Quote Originally Posted by zzephod View Post
    For the second two you should note that $\lim_{n \to \infty} a_n =1$ so they do not converge.

    .
    $\displaystyle\[{\lim _{x \to \infty }}\frac{{\sin \left( {{n^{ - 1}}} \right)}}{{{n^{ - 1}}}} = 1$
    Last edited by Plato; March 27th 2014 at 07:10 AM.
    Thanks from csc
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: December 9th 2012, 12:50 PM
  2. Replies: 2
    Last Post: May 22nd 2012, 05:57 AM
  3. Replies: 3
    Last Post: September 29th 2010, 06:11 AM
  4. Replies: 0
    Last Post: January 26th 2010, 08:06 AM
  5. Replies: 1
    Last Post: May 5th 2008, 09:44 PM

Search Tags


/mathhelpforum @mathhelpforum