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Derivative of infinite series

  1. Apr 28, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider the infinite series s(x)=1-tan^2(x)+tan^4(x)-tan^6(x)+... , where 0<x<pi/4
    s'(x)=
    A.sin2x
    B.cos2x
    C.-tan2x
    D.-sin2x
    E.-cos2x


    3. The attempt at a solution

    Attempting to derive the series, i get 1-2tanxsec^2x+4tan^3(x)sec^2(x)-6tan^5(x)sec^2(x)+...

    am i missing something obvious here? i don't see any trig identities in that that would give any of the answers
     
  2. jcsd
  3. Apr 28, 2012 #2

    LCKurtz

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    Hint: Sum that geometric series for s(x) first.
     
    Last edited: Apr 28, 2012
  4. Apr 28, 2012 #3
    i still can't get it :(
     
  5. Apr 28, 2012 #4

    Dick

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    What's the series expansion of 1/(1+r)?
     
  6. Apr 28, 2012 #5

    LCKurtz

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    Or what is the sum of a geometric series with first term a and ratio r?
     
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