(adsbygoogle = window.adsbygoogle || []).push({}); 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

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# Continuous and differentiable Of Cos

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