John D. Cook • 6/3/2026

Naively summing an alternating series

This article discusses the pitfalls of naively implementing the exponential function's power series for negative arguments, specifically exp(-20). It demonstrates how alternating series with large initial terms cause catastrophic cancellation and loss of precision, resulting in inaccurate results. The author explains the underlying floating-point limitations and suggests using 1/exp(20) as a simple workaround. The content is a technical tutorial focused on numerical analysis, programming, and mathematics, relevant to IT/technology.

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#Python #floating-point #Cancellation