Approximation of exponential function by power series – math.stackexchange.com

Let $x \in (-\frac{1}{2},\frac{1}{2}), n \in \mathbb{N}$ How can I choose a $n$ that the the inequality is valid? $$\left|e^x-\sum_{k=0}^n \frac{x^k}{k!}\right| \leq \frac{|e^x|}{10^{16}}$$ My ...

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