Thread: Taylor series of cos proof

Prove that the Taylor series for y = cos x, centred at 0, converges to cos x
for every x in R.

How would I do this?

You can use either the ratio test or the root test to show that the series converges for all .

That won't show that it converges to cos x though...wouldn't it just show whether it is convergent or not.

Nevermind, I'll assume I don't have to prove the Taylor series expansion of cos x converges to cos x.