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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Originally Posted by grabick_luca 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 05:49 AM.
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?