Lebl-Basic-Analysis-I · Problem 5.4.3

The Riemann Integral

Mathematics · logarithm-exponential

Problem

(requires §4.3) Use Taylor's theorem to study the remainder term and show that for all

x \in \mathbb{R}

e^x = \sum_{n=0}^\infty \frac{x^n}{n!}.

Hint: Do not differentiate the series term by term (unless you would prove that it works).