#1612 · Real Analysis · Series

Logarithmic Relation Proof

Show that $lo g_{e} (x + 2 h) = 2 lo g_{e} (x + h) - lo g_{e} x - {\frac{h ^{2}}{( x + h ) ^{2}} + \frac{h ^{4}}{2 ( x + h ) ^{4}} + \frac{h ^{6}}{3 ( x + h ) ^{6}} + \dots}$ .

~15 minProof · checked by AILogarithmic seriesAlgebraic manipulation

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XVII. Exponential and Logarithmic Series, Examples XVII, No. 16

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