Howe to multiply two power series?

Question

I have e^-x and cos(x), which works out to be

e^-x= 1- x + (x^2)/(2!) - (x^3)/(3!) +...

cos(x)= 1 - (x^2)/(2) + (x^4)/(4) - (x^6)/(6) + ...

How do I multiply the two?

1*1 then 1* (- (x^2)/(2) )?

or 1*1, (- (x^2)/(2) )*(x^2)/(2!) ?

Answer 1

Make a taylor series for (e^-x*cos(x)) is one way you could do it.

Answer 2

Find the power series of the function f(x)= e^-(x)*cos(x).It is much easier than mutliplying separately.