Results 1 to 6 of 6

Math Help - Alternate Series Test

  1. #1
    Junior Member
    Joined
    Jan 2009
    Posts
    39

    Alternate Series Test

    ((-1)^(n+1)*n^(2)*3^n)/2^n

    can anyone help me with this problem. i tried the alternating series test and it came out inconclusive, but i don't know what other test to try.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    lim (n^2)*(3^n)/2^n = lim n^2 (3/2)^n = inf

    Therefore the series diverges
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2009
    Posts
    39
    whats the condition to prove that. just because the series equals 0, then it diverges?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    The alt series test

    For (-1)^n an if an is a decreasing seq

    If lim an = 0 then the series converges

    If lim an is not 0 (regardless of whether or not it is decreasing) the series diverges this is because the sequence diverges

    Remember for any series if the sequence doesn't converge to 0 the series diverges

    If you want go to my website where i illustrate with animations alternating sequences

    Infinite Sequences
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member woof's Avatar
    Joined
    Apr 2009
    Posts
    31
    Quote Originally Posted by needhelp101 View Post
    whats the condition to prove that. just because the series equals 0, then it diverges?
    The alt series test does not apply, since that is a test whose conclusion can only tell you about convergence. It's the one sentence above that gives you the justification:


    If lim an is not 0 (regardless of whether or not it is decreasing) the series diverges.

    The above is true whether the series alternates or not.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member redsoxfan325's Avatar
    Joined
    Feb 2009
    From
    Swampscott, MA
    Posts
    943
    Quote Originally Posted by needhelp101 View Post
    ((-1)^(n+1)*n^(2)*3^n)/2^n

    can anyone help me with this problem. i tried the alternating series test and it came out inconclusive, but i don't know what other test to try.
    a_n = (-1)^{n+1}n^2\left(\frac{3}{2}\right)^n

    This is unbounded and therefore \sum_{n=1}^{\infty}a_n diverges.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Convergence of the alternate harmonic series
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: March 19th 2011, 04:13 PM
  2. Alternate series converges
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: June 16th 2010, 01:40 PM
  3. Replies: 7
    Last Post: June 4th 2009, 10:33 PM
  4. ratio test (series) urgent test tommorow!
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 2nd 2008, 04:27 PM
  5. alternate series question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 18th 2007, 10:39 AM

Search Tags


/mathhelpforum @mathhelpforum