Results 1 to 3 of 3

Math Help - absolutely convergent, conditionally convergent or divergent

  1. #1
    Junior Member
    Joined
    Jul 2009
    Posts
    42

    absolutely convergent, conditionally convergent or divergent

    the question is: determine whether the series is absolutely convergent, conditionally convergent or divergent.

    \sum_{n = 1}^{\infty} (-3)^n \frac{n+1}{\exp(n)}

    I found that if i do the ratio test it diverges but im not sure how to do the alternating test, is a just

    \frac{n+1}{\exp(n)}

    or does it include the 3?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,130
    Thanks
    1012
    Quote Originally Posted by acosta0809 View Post
    the question is: determine whether the series is absolutely convergent, conditionally convergent or divergent.

    \sum_{n = 1}^{\infty} (-3)^n \frac{n+1}{\exp(n)}

    I found that if i do the ratio test it diverges but im not sure how to do the alternating test, is a just

    \frac{n+1}{\exp(n)}

    or does it include the 3?

    ratio test ...


    \lim_{n \to \infty} \left| \frac{(-3)^{n+1}(n+2)}{e^{n+1}} \cdot \frac{e^n}{(-3)^n (n+1)}\right|

    \lim_{n \to \infty} \left| \frac{(-3)(n+2)}{e(n+1)}\right|

    \left|\frac{-3}{e}\right| \lim_{n \to \infty} \frac{n+2}{n+1}

    \left|\frac{-3}{e}\right| \cdot 1 > 1

    series diverges
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    14
    For each n\ge1 it's \frac{3^{n}(n+1)}{e^{n}}>n+1, so this is far to converge absolutely.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: May 2nd 2010, 04:25 AM
  2. Replies: 1
    Last Post: April 25th 2010, 09:46 PM
  3. Replies: 5
    Last Post: January 19th 2010, 10:54 AM
  4. Replies: 3
    Last Post: April 6th 2009, 11:03 PM
  5. Replies: 8
    Last Post: February 21st 2009, 10:16 AM

Search Tags


/mathhelpforum @mathhelpforum