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Math Help - Maclaurin Expansions

  1. #1
    grabick_luca
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    Maclaurin Expansions

    Could you please help
    prove the expansion. cos x = 1 - x^2/2! + x^4/4! - x^6/6! ..... + (-1)^n x^2n/(2n)! + .....


    Thank You
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by grabick_luca View Post
    Could you please help
    prove the expansion. cos x = 1 - x^2/2! + x^4/4! - x^6/6! ..... + (-1)^n x^2n/(2n)! + .....


    Thank You
    The MacLaurin series for f(x) is:

    f(x) = f(0) + f'(0) x /1! + f''(0) x^2 /2! + .... f^(n) x^n /n! + ...

    Now D^(2n) cos(x) = (-1)^n cos(x), and D^(2n-1) cos(x) = (-1)^n sin(x).

    and the result follows.

    RonL
    Last edited by CaptainBlack; March 1st 2007 at 06:49 AM.
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  3. #3
    Super Member

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    Hello, grabick_luca!

    Prove the expansion:
    . . cos x .= .1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + ... + (-1)^n (x^{2n})/(2n)! + .....

    Are you supposed to derive the expansion by the Maclaurin procedure?

    If you know the procedure, what's stopping you?

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