#1617 · Real Analysis · Series

Logarithmic Difference Series

Prove that $2 lo g_{e} n - lo g_{e} (n + 1) - lo g_{e} (n - 1) = \frac{1}{n ^{2}} + \frac{1}{2 n ^{4}} + \frac{1}{3 n ^{6}} + \dots$ .

~12 minProof · checked by AILogarithmic series

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XVII. Exponential and Logarithmic Series, Examples XVII, No. 22

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