#1614 · Real Analysis · Series

Logarithm Expansion Involving n

Show that $lo g_{e} (1 + \frac{1}{n})^{n} = 1 - \frac{1}{2 ( n + 1 )} - \frac{1}{2 \cdot 3 ( n + 1 ) ^{2}} - \frac{1}{3 \cdot 4 ( n + 1 ) ^{3}} - \dots$ .

~15 minProof · checked by AILogarithmic seriesExpansions

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XVII. Exponential and Logarithmic Series, Examples XVII, No. 19

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