Thread: 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

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

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?