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| Logarithmic Series |
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 If x is a real number such that |x|<1, then the series is
called the logarithmic series. It can be proved mathematically that this logarithmic series has the sum equal to log(1 + x). |
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| Since |x|<1, we have by binomial theorem, |
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 Comparing, the coefficients of y in (1) and (2), we get |
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| Remark: |
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| The terms in log(1 + x) carry alternatively positive and negative signs. The terms in log(1 + x) do not involve factorials as in the exponential series. |
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Exponential and Logarithmic Series
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