#1600 · Real Analysis · Series

Sum of a Logarithmic Series with Base 2

Find the value of the series $\frac{1}{2} - \frac{1}{2 \cdot 2 ^{2}} + \frac{1}{3 \cdot 2 ^{3}} - \frac{1}{4 \cdot 2 ^{4}} + \frac{1}{5 \cdot 2 ^{5}} - \dots$ .

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H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XVII. Exponential and Logarithmic Series, Examples XVII, No. 2

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).