Results 1 to 2 of 2

Math Help - Sigma Notation

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    3

    Sigma Notation

    Consider the series the sum of x^-n for values of n from 1 to infinity.
    Looks kinda like that:

    infinity
    sigma x^-n.
    n=1

    a) What is the interval of convergence?
    b) In terms of x, find the sum of the series.

    I have no idea how to find the interval of convergence
    I tried making charts where x =1 and I'd go
    n = 1, x^-n = 1
    n = 2, x^-n = 1/1^2 = 1
    n = 3, x^-n = 1/1^3 = 1
    ....
    ...
    and then x = 2
    n = 1, x^-n = 1/2
    n = 2, x^-n = 1/2^2 = 1/4
    n = 3, x^-n = 1/2^3 = 1/8
    ...
    ...
    I'm assuming the interval of convergence is when my outputs start becoming positive and negative. (ex: -1, 2, -3, 4...)

    Then for B, I tried using the sequence formula of adding the sum of an infinite geometric sequence.
    I did: Sn = T1 / 1-r
    = X^-1 / 1-(-n)
    = 1/x / 1+n
    = 1/x * 1+n/1 = 1+n / x

    Help would be greatly appreciated, thank you!

    ~Wingless
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Amer's Avatar
    Joined
    May 2009
    From
    Jordan
    Posts
    1,093
    \sum_{n=1}^{\infty}\frac{1}{x^n}

    if -1<x<1 how the series will be ??

    \left(\frac{1}{\frac{1}{2}}\right)^{n}=??

    if you know how it will be when -1<x<1 and when x in [1,infinity) or (-infinity,-1]


    use ratio or root test then you will get the convergence interval
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. sigma notation
    Posted in the Algebra Forum
    Replies: 3
    Last Post: June 24th 2010, 09:35 AM
  2. Sigma Notation Help
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: February 27th 2010, 12:15 AM
  3. Sigma notation help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 29th 2009, 07:07 PM
  4. sigma notation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 14th 2009, 04:17 PM
  5. Sigma notation
    Posted in the Algebra Forum
    Replies: 5
    Last Post: January 24th 2008, 03:30 AM

Search Tags


/mathhelpforum @mathhelpforum