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# Prove that the series obtained in Exercise 13 represents $\cos x$ for all $x.$

## $$\lim _{n \rightarrow \infty} R_{n}(x)=0$$

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The problem is proof that Siri's of changing exercise thirteen represents co sign Axe for or Axe in exercise. Thirteen. We're half So my Clarence theories focus on tax. This sum from zero to infinity. Nick, do you want to end hams? Axe to two and over two in Factorial so we can say this is on alternating Siri's. So the art imitating Siri's estimation theory, um shows as Eric involved in this approx approximation our two and x this last time axe too. Shoot. Perhaps I'm plus one over to M plus one Factorial. Yeah, you have squalor you smaller than this one. And this thing is the limit on goes to infinity access to M plus two over two and plus two bacterial secret zero. It's over half lim our two and my hand cost to infinity is equal to zero so that there is a change in exercise. Thirteen. This Siri's represents Kasan axe or axe

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