1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Series expansion

  1. Oct 16, 2013 #1
    1. The problem statement, all variables and given/known data
    Show that 1- x/2 + x^2/3 - x^3/4 + x^4/5.... (-1)^n (x^n)/(n+1) = ln(1+x)/x
    with |x| < 1

    2. Relevant equations

    3. The attempt at a solution
    finding derivative of the function multiplied by x
    = 1 -x + x^2 - x^3 + x^4 - x^5 +....

    absolute value of this function = 1 + x + x^2 + x^3 + x^4.... = 1/1-x ( geometric series)
    the integral of that gives us -ln(1-x) + c

    drawing a blank now. not really sure where to go.
  2. jcsd
  3. Oct 16, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    No it isn't. But it is a geometric series, so you can sum it quite easily.
  4. Oct 16, 2013 #3
    ok the absolute value part is wrong, but what do you mean i can sum it up easily? i dont get it. is the integral still -ln(1-x) + c..? i know the geometric series for 1 + x + x^2 + .... = 1/1-x, but how does that change with alternating signs? is it going to be (-1)^n*(1/1-x)? so the integral is (-1)^n*-ln(1-x)? how do i go from that to ln(1+x)/x?
    Last edited: Oct 16, 2013
  5. Oct 16, 2013 #4


    User Avatar
    Science Advisor

    An alternating series involves (1)n which can easily be incorported into the geometric series.
  6. Oct 16, 2013 #5


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I think you meant (-1)n.
    Thercias, what is the ratio of consecutive terms in your alternating series? If it's independent of n then it's a geometric series.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Series expansion
  1. Series expansion (Replies: 3)

  2. Series expansion (Replies: 6)

  3. Series Expansions (Replies: 1)

  4. Series expansions (Replies: 5)