# Math Help - Taylor Series (check my answer plz)

1. ## Taylor Series (check my answer plz)

Find the infinite Taylor Series representation for f(x) = cos(2x), centered
at C = pi/4

This is what I got, not too sure about the correctness of it haha.

wish I knew how to write in that neat math font...anyway

Summation of 0 to infinity = ((-1)*2^n)/((2n)!) * (x-(pi/4))^(2n)

thanks.

2. Originally Posted by Grimey
Find the infinite Taylor Series representation for f(x) = cos(2x), centered
at C = pi/4

This is what I got, not too sure about the correctness of it haha.

wish I knew how to write in that neat math font...anyway

Summation of 0 to infinity = ((-1)*2^n)/((2n)!) * (x-(pi/4))^(2n)

thanks.
I get $-2\bigl(x-\tfrac\pi4\bigr) + \frac{8\bigl(x-\tfrac\pi4\bigr)^3}{3!} - \frac{32\bigl(x-\tfrac\pi4\bigr)^5}{5!} + \ldots = \sum_{n=0}^\infty\frac{(-1)^{n-1}2^{2n+1}}{(2n+1)!} \bigl(x-\tfrac\pi4\bigr)^{2n+1}$.