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Power series help

  1. Nov 1, 2004 #1
    Can anyone help me with this? It's been really annoying me and I think I am just forgetting something:

    Using the series expansion for cosx in powers of x find the first four non-zero terms of the corresponding series for sec x.

    I get obviously that as secx is 1/cosx it is a case of division of power series but I get confused because it is 1/a power series rather than a power series/a power series so I'm not sure how to treat this.

    I would really appreciate help.
  2. jcsd
  3. Nov 1, 2004 #2


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    Basically you want to expand this:

    [tex]\frac {1}{1-stuff}[/tex]

    which you can expand into

    [tex] 1 + stuff + stuff^2 + stuff^3 + O(stuff^4)[/tex]

    and you'll do a lot of algebra to expand the powers of stuff all of which must contain several terms in powers of x. Enjoy!
  4. Nov 1, 2004 #3

    Thankyou very much. I will give it a go :)
  5. Nov 3, 2004 #4
    Okay, get the maclaurin expansion for cosx

    namely, 1-x^2/2 + x^4/4! -...

    Then write (1+(x^4/4! -x^2/2+...) for cos x

    Since sec x =(cosx)^-1 you can now use the binomial theorem to deduce the series for secx


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