Results 1 to 9 of 9

Math Help - Infinite Series, why divergent and not convergent?

  1. #1
    Newbie
    Joined
    Feb 2010
    From
    Canada
    Posts
    7

    Infinite Series, why divergent and not convergent?

    hey guys, I am facing the following problem:

    Determine whether the series is convergent or divergent:




    The answer in my book says that it is divergent but I do not understand why and how they got to that answer? any help would be greatly appreciated!

    thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,628
    Thanks
    430
    Quote Originally Posted by dmitrip View Post
    hey guys, I am facing the following problem:

    Determine whether the series is convergent or divergent:

    <br />
\sum_{n=1}^{\infty} \frac{1}{2n}<br />


    The answer in my book says that it is divergent but I do not understand why and how they got to that answer? any help would be greatly appreciated!

    thank you!
    because <br />
\frac{1}{2} \sum_{n=1}^{\infty} \frac{1}{n}<br />
is divergent.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2010
    From
    Canada
    Posts
    7
    thanks for the reply but how do you know that? I thought if I use the test for divergence and take the limit of 1/n, the limit will approach 0 , so wouldn't that mean that it is convergent?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Apr 2008
    Posts
    1,092
    Quote Originally Posted by dmitrip View Post
    thanks for the reply but how do you know that? I thought if I use the test for divergence and take the limit of 1/n, the limit will approach 0 , so wouldn't that mean that it is convergent?
    No. The nth term test says that if the limit of the sequence of terms in the series is not 0, then the series diverges. It says nothing if that limit is 0.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Feb 2010
    From
    Canada
    Posts
    7
    Quote Originally Posted by icemanfan View Post
    No. The nth term test says that if the limit of the sequence of terms in the series is not 0, then the series diverges. It says nothing if that limit is 0.
    ok I understand that but then how do you know that is divergent?

    thanks
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by dmitrip View Post
    thanks for the reply but how do you know that? I thought if I use the test for divergence and take the limit of 1/n, the limit will approach 0 , so wouldn't that mean that it is convergent?
    The "sequence", which is the list of terms, converges.
    The 'series" which is the sum of the terms of the sequence, doesn't.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Apr 2008
    Posts
    1,092
    Quote Originally Posted by dmitrip View Post
    ok I understand that but then how do you know that is divergent?

    thanks
    The series \sum_{n=1}^\infty \frac{1}{n} is a well-known series called the Harmonic series, and it diverges. Using the fact that any nonzero constant multiple of a divergent series also diverges, we have the result given by skeeter.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,628
    Thanks
    430
    you need to do some research on the divergence of the harmonic series ...

    http://faculty.prairiestate.edu/skif...cs/harmapa.pdf
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Feb 2010
    From
    Canada
    Posts
    7
    Thanks guys.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: March 29th 2010, 11:36 AM
  2. Infinite Series: Divergent or Convergent?
    Posted in the Calculus Forum
    Replies: 6
    Last Post: October 26th 2009, 08:37 PM
  3. Replies: 3
    Last Post: April 6th 2009, 10:03 PM
  4. Replies: 8
    Last Post: February 21st 2009, 09:16 AM
  5. Infinite series - convergent vs divergent
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 20th 2007, 07:59 AM

Search Tags


/mathhelpforum @mathhelpforum