Results 1 to 4 of 4

Math Help - series problem

  1. #1
    Newbie
    Joined
    Nov 2006
    Posts
    10

    series problem

    does this converge or diverge, if it converges, to what sum.

    (2/3) - (4/9) + (8/27) - (16/81)

    so a(n) = (-1)^n * 2^(n+1)/3^(n+1)

    i know its convergent by alternating series test, but how can i figure out what sum it converges to without Sn formula?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by synnexster View Post
    does this converge or diverge, if it converges, to what sum.

    (2/3) - (4/9) + (8/27) - (16/81)

    so a(n) = (-1)^n * 2^(n+1)/3^(n+1)

    i know its convergent by alternating series test, but how can i figure out what sum it converges to without Sn formula?
    It is a geometric series,
    The ratio is,
    -2/3
    Which is convergent since,
    |-2/3|<1
    Now just use the infinite geometric sum formula to find the sum.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2006
    Posts
    10
    so the sum would be a/(1-r) right?
    so (2/3)/(1-(2/3)) = 2
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by synnexster View Post
    so the sum would be a/(1-r) right?
    so (2/3)/(1-(2/3)) = 2
    Indeed, I shall wager my soul for that!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sum of series problem #2
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 5th 2011, 01:20 PM
  2. Sum of series problem #1
    Posted in the Calculus Forum
    Replies: 6
    Last Post: December 5th 2011, 12:17 PM
  3. Replies: 3
    Last Post: September 29th 2010, 06:11 AM
  4. Series Problem
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 7th 2010, 01:02 AM
  5. Replies: 0
    Last Post: January 26th 2010, 08:06 AM

Search Tags


/mathhelpforum @mathhelpforum