Tea Time Numerical Analysis · Problem 1.2.31

Preliminaries — Leon Brin

Mathematics — Numerical Analysis · maclaurin-series

Problem

The Maclaurin Series for

f(x) = e^{-x}

\sum_{i=0}^{\infty} \frac{(-1)^i}{i!} x^i = 1 - x + \frac{1}{2}x^2 - \frac{1}{6}x^3 + \ldots

Find a bound on the error in approximating

1/e

1 - 1 + 1/2 - 1/6 + 1/24