Results 1 to 2 of 2

Thread: alternating series

  1. April 26th 2010, 10:01 PM #1
    Brotha
    Brotha is offline
    Newbie
    Joined
    Apr 2010
    Posts
    11

    alternating series

    sum_(n=-1)^infinity(-1)^(n+1) (1/3)^n = 9/4~~2.25...

    How do you prove that? Is there a certain formula to figure out the sum of the alternating series?
    Follow Math Help Forum on Facebook and Google+
  2. April 26th 2010, 10:37 PM #2
    Chris L T521
    Chris L T521 is offline
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Santa Cruz, CA
    Posts
    2,845
    Thanks
    2
    Quote Originally Posted by Brotha View Post
    sum_(n=-1)^infinity(-1)^(n+1) (1/3)^n = 9/4~~2.25...

    How do you prove that? Is there a certain formula to figure out the sum of the alternating series?
    It appears to be geometric in form. Observe that:

    \sum_{n=-1}^{\infty}(-1)^{n+1}\left(\tfrac{1}{3}\right)^n=3-\sum_{n=0}^{\infty}\left(-\tfrac{1}{3}\right)^n=\ldots

    Can you finish this?
    Follow Math Help Forum on Facebook and Google+
« Position Function Question | partial derivative question »

Similar Math Help Forum Discussions

  1. Alternating series
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 5th 2010, 07:43 AM
  2. Alternating series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 31st 2010, 10:44 PM
  3. Alternating Series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 26th 2009, 03:37 AM
  4. Alternating Series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 20th 2008, 12:10 PM
  5. Alternating Series
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 8th 2008, 11:03 PM

Search Tags


/mathhelpforum @mathhelpforum