# The taylor series about 0 for the function f(x)=cos (x) ?

##### 1 Answer

Mar 12, 2018

The coefficient is

#### Explanation:

We seek the coefficient of

#f(x)=cos(x)*1/(1-x)#

Using

#cos(x)=(1-x^2/2+x^4/24+...)# #1/(1-x)=(1+x+x^2+x^3+...)#

We can write this as

#f(x)=(1-x^2/2+x^4/24+...)(1+x+x^2+x^3+...)#

Notice the only terms involving

is obtained by

#x^3+(-x^2/2)*x=x^3-x^3/2=color(blue)(1/2)x^3#