Consider the Taylor series expansion of ##e^{-x}## as follows:(adsbygoogle = window.adsbygoogle || []).push({});

##\displaystyle{e^{-x}=1-x+\frac{x^{2}}{2}-\frac{x^{3}}{6}+\dots}##

For ##x>0##, the partial sums ##1##, ##1-x##, ##\displaystyle{1-x+\frac{x^{2}}{2}}## bound ##e^{-x}## from above and from below alternately.

How do I prove this?

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# I Alternating partial sums of a series

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