#1727 · Algebra · Polynomials

Sum of Products of Powers

Shew that the sum of the products $n - r$ together of the $n$ quantities $a, a^2, a^3,
ot ext{dots}, a^n $i s$ \dfrac{(a^{r+1}-1)(a^{r+2}-1)\dots(a^n-1)}{(a-1)(a^2-1)\dots(a^{n-r}-1)} a^{\frac{1}{2}(n-r)(n-r+1)}$.

~30 minProof · checked by AIsymmetric functionsseries of powers

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXII. Undetermined Coefficients, Examples XXII.a, No. 15

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