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The Taylor series for cosx can be found by differentiating [itex] sum_{k=0}^{\infty} \frac{(-1)^k (x^{2k+1})}{(2k+1)!}[/itex] on both sides...

But I'm not sure what the question means by "why it converges to cosx for all x in R". Isn't that just obvious, since the summation equals cosx...it obviously converges to it...

Thanks in advance