#1733 · Algebra · Sequences & series

Coefficients in Rational Expansion

Find $a$ , $b$ , and $c$ so that the coefficient of $x^{n}$ in the expansion of $\frac{a + b x + c x ^{2}}{( 1 - x ) ^{3}}$ in ascending powers of $x$ is $n^{2} + 1$ .

~10 minAnswer checked instantlyUndetermined coefficientsGenerating functionsBinomial theorem

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXII. Undetermined Coefficients, Examples XXII.b, No. 7

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