#1615 · Real Analysis · Series

Coefficient of x^n in Logarithm Expansion

If $lo g_{e} \frac{1}{1 + x + x ^{2} + x ^{3}}$ be expanded in a series of ascending powers of $x$ , shew that the coefficient of $x^{n}$ is $- \frac{1}{n}$ if $n$ be odd, or of the form $4 m + 2$ , and $\frac{3}{n}$ if $n$ be of the form $4 m$ .

~20 minProof · checked by AIPower seriesLogarithmic series

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XVII. Exponential and Logarithmic Series, Examples XVII, No. 20

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