Find the Maclaurin expansion of cos(x^3)

Question

anonymous · Answer

So i'm thinking since it's Maclaurin a = 0.
I know the Maclaurin expansion of cos(x) = SUM(-1)^n * (x^(2n))/(2n)!

anonymous · Answer

replace x with x^3

anonymous · Answer

why would we just do that ? if it was asking for the maclaurin expansion of x cos (x) i would just multiply the expansion of cos(x) by x. So wouldn't I need to multiply it by something again or do some computation to the orignal expansion besides just replacing x ?

anonymous · Answer

just replacing

anonymous · Answer

for example u know that       $ \frac{1}{1-x}=1+x+x^2+... $   for |x|<1  now for  $ \frac{1}{1-x^2}$  u just need to replace x with x^2  to get $ \frac{1}{1-x^2}=1+x^2+x^4+... $

anonymous · Answer

oh wow. I get it now. sorry for making you have to type up those equations. Thanks though!

anonymous · Answer

welcome my friend