Category:Definitions/Newton-Mercator Series
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This category contains definitions related to Newton-Mercator Series.
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Let $\ln x$ denote the natural logarithm function.
Then:
| \(\ds \map \ln {1 + x}\) | \(=\) | \(\ds x - \dfrac {x^2} 2 + \dfrac {x^3} 3 - \dfrac {x^4} 4 + \cdots\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \sum_{n \mathop = 1}^\infty \frac {\paren {-1}^{n + 1} } n x^n\) |
The series converges to the natural logarithm (shifted by $1$) for $-1 < x \le 1$.
This is known as the Newton-Mercator series.
Pages in category "Definitions/Newton-Mercator Series"
The following 5 pages are in this category, out of 5 total.