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Ed Quanta
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What is Tannery's Theorem? I can't seem to find a definition of what it is. And how do you use it?
Tannery's Theorem, also known as the Tannery-Steinhardt Theorem, is a mathematical theorem that relates to the convergence of series. It states that if a series of real or complex numbers satisfies certain conditions, then the series must either converge absolutely or diverge.
Jules Tannery was a French mathematician who developed this theorem in the late 19th century. He published it in his paper "Sur la convergence des séries", which was presented to the French Academy of Sciences in 1893.
The conditions for Tannery's Theorem are as follows:
Tannery's Theorem is useful in determining the convergence or divergence of series in mathematics. It can be used to simplify the process of determining the convergence of a series by eliminating the need to use other convergence tests.
No, Tannery's Theorem can only be applied to series that meet the specific conditions outlined in the theorem. If a series does not meet these conditions, then Tannery's Theorem cannot be used to determine its convergence or divergence.