#1031 · Algebra · Sequences & series

Sum of complicated infinite series

Find the sum of the infinite series $1 + (1 + b) r + (1 + b + b^{2}) r^{2} + (1 + b + b^{2} + b^{3}) r^{3} + \dots$ , where $r$ and $b$ are proper fractions.

~12 minAnswer checked instantlyinfinite seriesgeometric series

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. V. Geometrical Progression, Examples V.b, No. 9

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