TIFR-2013-Maths-B: 18

Question

True/False Question :

Let $P\left ( x \right )=1+x+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}+\cdots +\frac{x^{n}}{n!}$ where $n$ is a large positive integer. Then $\underset{x\rightarrow \infty }{lim}\:\frac{e^{x}}{p\left ( x \right )}=1.$