#1498 · Algebra · Linear equations

Coefficient Periodic Pattern

Prove that the coefficient of $x^{n}$ in the expansion of $\frac{1}{1 + x + x ^{2}}$ is $1, 0, - 1$ according as $n$ is of the form $3 m$ , $3 m - 1$ , or $3 m + 1$ .

~15 minProof · checked by AIGenerating FunctionsPower Series

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIV. Binomial Theorem: Any Index, Examples XIV.c, No. 15

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