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?
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You can use either the ratio test or the root test to show that the series converges for all $\displaystyle x$.
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.
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