Leonard Euler Found the Following Series to Be Noteworthy Because $\pi$

question 44

Essay

Leonard Euler found the following series to be noteworthy because it is part of a process that can be used to approximate $\pi$ : $1-\frac{1}{3 \cdot 64}+\frac{1}{5 \cdot 64^{2}}-\frac{1}{7 \cdot 64^{3}}+\frac{1}{9 \cdot 64^{4}}-\ldots$
(a)Re-write this series in summation notation.
(b)Use an appropriate test to show that the series converges.

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Definitions:

Scrap

Waste material or any unwanted item that can be removed from a process, often recycled or sold to reclaim value.

End Items

Final products ready for sale or consumed as a completed part of a project or commodity.

Sheet Metal

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Mixed Integer Linear Optimization Model

An optimization technique involving mathematical formulas that aim to find the best outcome in a model with both integer and continuous variables under linear relationships.