# Continuous and differentiable Of Cos

1. Dec 2, 2008

### kala

1. The problem statement, all variables and given/known data
how could i prove that cos x= sum (n=1 to 00) [((-1)^n) * x^(2n)/((2n)!)]
is continuous and differentiable at each x in R

2. Relevant equations
the Taylor Expansion of cosine is the given equation

3. The attempt at a solution
basically i need to prove that the Taylor expansion of cos is differentiable and continuous. I think i need to use the Weierstrass M-test, however i could not figure out what M_n was, is there a different way to go about this one, or any suggestions for M_n

2. Dec 2, 2008