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Mercator series : ウィキペディア英語版
Mercator series
In mathematics, the Mercator series or Newton–Mercator series is the Taylor series for the natural logarithm:
:\ln (1+x) \;=\; x \,-\, \frac \,+\, \frac \,-\, \frac \,+\, \cdots.
In summation notation,
:\ln (1+x) \;=\; \sum_^\infty \frac x^n.
The series converges to the natural logarithm (shifted by 1) whenever −1 < ''x'' ≤ 1.
==History==
The series was discovered independently by Nicholas Mercator, Isaac Newton and Gregory Saint-Vincent. It was first published by Mercator, in his 1668 treatise ''Logarithmotechnia''.

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