#1606 · Real Analysis · Series

Logarithmic power series identity

Prove that $lo g_{e} (1 + x)^{1 + x} (1 - x)^{1 - x} = 2 (\frac{x ^{2}}{1 \cdot 2} + \frac{x ^{4}}{3 \cdot 4} + \frac{x ^{6}}{5 \cdot 6} + \dots)$ .

~15 minProof · checked by AILogarithmic seriesPower series expansion

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XVII. Exponential and Logarithmic Series, Examples XVII, No. 8

Stuck? A gentle nudge

Something off?

Workspace

Your working

Check your full solution

Upload photos of your handwritten work or a PDF, and Lemma will read it and tell you whether it's right — and where it first goes wrong if not.