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Proposition: Estimate for the Remainder Term of Exponential Function
The absolute value of the remainder term \(r_{N + 1}(x)\) of the exponential series.
\[r_{N + 1}(x):=\sum_{n=N+1}^\infty\frac{x^n}{n! }\]
can be estimated by the inequation
\[
|r_{N + 1}(x)|\le 2\frac{|x|^{N+1}}{(N+1)!}\quad\text{for }|x|\le \frac {N+2}2.\]
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References
Bibliography
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
