I was encountered following example.In that I do not understand Last part.
I do not understand following . Why such adjustment has been done? Any Help will be appreciated
$$E(z)=-\left(\dfrac{1}{2!}+\dfrac{iz}{3!}+\dfrac{(iz)^2}{4!}+\cdots\right)$$ then $$|E(z)|\leq\dfrac{1}{2!}+\dfrac{|z|}{3!}+\dfrac{|z|^2}{4!}+\cdots\to\dfrac12$$ as $z\to0$.
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$$E(z)=-\left(\dfrac{1}{2!}+\dfrac{iz}{3!}+\dfrac{(iz)^2}{4!}+\cdots\right)$$ then $$|E(z)|\leq\dfrac{1}{2!}+\dfrac{|z|}{3!}+\dfrac{|z|^2}{4!}+\cdots\to\dfrac12$$ as $z\to0$.