Results 1 to 2 of 2

Math Help - Alternating Series

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    2

    Alternating Series

    consider the series:
    n=1 infinity
    (-1)^n/( sqrt(n) +1) or

    n=1 infinity
    (-1)^n/(n!)^2

    I understand that these series satisfy the alternating series test.

    How many terms need to be added in order to reach within 10^-8 of the sum of the series?

    I also need to figure out how to give a decimal approximation of the sum of one of these series with the maximum allowed error of 10^-8.

    Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by brdun3 View Post
    consider the series:
    n=1 infinity
    (-1)^n/( sqrt(n) +1) or

    n=1 infinity
    (-1)^n/(n!)^2

    I understand that these series satisfy the alternating series test.

    How many terms need to be added in order to reach within 10^-8 of the sum of the series?

    I also need to figure out how to give a decimal approximation of the sum of one of these series with the maximum allowed error of 10^-8.

    Thank you!
    Let S=\sum_{n=0}^{\infty}(-1)^na_n and S_N=\sum_{n=0}^{N}(-1)^na_n, then R_N=\left|S-S_N\right|\leqslant{a_{N+1}}. In other words the amount of error is less than or equal to the first neglected term.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. alternating series help
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 29th 2011, 05:28 PM
  2. alternating series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 26th 2010, 11:37 PM
  3. Alternating series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 31st 2010, 11:44 PM
  4. alternating series
    Posted in the Math Challenge Problems Forum
    Replies: 1
    Last Post: August 2nd 2009, 05:17 AM
  5. Alternating Series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 26th 2009, 04:37 AM

Search Tags


/mathhelpforum @mathhelpforum