#1037 · Algebra · Sequences & series

Alternating geometric series with two bases

Find the sum to infinity of the series $\frac{4}{7} - \frac{5}{7 ^{2}} + \frac{4}{7 ^{3}} - \frac{5}{7 ^{4}} + \frac{4}{7 ^{5}} - \frac{5}{7 ^{6}} + \dots$ .

~3 minAnswer checked instantlyGeometric seriesInfinite sum

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. V. Geometrical Progression, Examples V.b, No. 16

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