1. Not finding help here? Sign up for a free 30min 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 to represent alternate between 1 and -1

  1. May 8, 2016 #1
    1. The problem statement, all variables and given/known data
    we know that a2 , a4 ,a6 (even number ) = 0 , but when a1 , a3 , a5 (odd numbers) , the answer of an alternate between positive and negative .... in the second circle , the author represent it with (-1)^(n+1) , i dont think this is correct , this is because when n=3 , an = -2/ 3pi when n=3 , [ (-1) ^(3+1 ) ] = positive 1 , not negative 1 !!! can someone explain on this ?
    OW5ijzU.jpg
    o9H3EwT.jpg

    2. Relevant equations


    3. The attempt at a solution
     
  2. jcsd
  3. May 8, 2016 #2

    stevendaryl

    User Avatar
    Staff Emeritus
    Science Advisor

    I think that the author redefined [itex]n[/itex]. To make it clear, you start off assuming that

    [itex]f(x) = a_0 + \sum_n a_n cos(nx)[/itex]

    Then, for this particular problem, you find that for [itex]n > 0[/itex], then [itex]a_n = 0[/itex] unless [itex]n[/itex] is odd. If [itex]n[/itex] is odd, then that means that [itex]n[/itex] can be written as:

    [itex]n = 2n'-1[/itex]

    where [itex]n' = 1, 2, 3, ...[/itex]

    So the term [itex]-\frac{2}{\pi} \frac{cos(3x)}{1}[/itex] corresponds to [itex]n=3[/itex], but it corresponds to [itex]n' = 2[/itex]. In terms of [itex]n'[/itex], the general term is

    [itex]\frac{2}{\pi} \frac{cos((2n'-1)x)}{2n'-1} (-1)^{n'+1}[/itex]
     
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 to represent alternate between 1 and -1
  1. Alternating Series (Replies: 1)

  2. Alternating Series (Replies: 2)

  3. Alternating Series (Replies: 5)

  4. Alternating series (Replies: 2)

Loading...