#1892 · Algebra · Sequences & series

Sum of series with telescoping terms II

Find the sum of $n$ terms of the series $\frac{x ( 1 - a x )}{( 1 + x ) ( 1 + a x ) ( 1 + a ^{2} x )} + \frac{a x ( 1 - a ^{2} x )}{( 1 + a x ) ( 1 + a ^{2} x ) ( 1 + a ^{3} x )} + \dots$

~20 minAnswer checked instantlyTelescoping seriesPartial fractions

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXIII. Partial Fractions, Examples XXIII, No. 23 (part 2)

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