Problem 786 (difficulty: 5/10)

Let \(\displaystyle x<0\) and \(\displaystyle n\) positive integer. Which one is the greater? \(\displaystyle e^x\) or \(\displaystyle 1+\dfrac{x}{1!}+\dfrac{x^2}{2!}+\ldots+\dfrac{x^n}{n!}\)?

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