#1531 · Algebra · Linear equations

Alternating Binomial Coefficient Identity

If $c_{0}, c_{1}, c_{2}, \dots, c_{n}$ are the coefficients in the expansion of $(1 + x)^{n}$ for a positive integer $n$ , prove that $c_{0} - c_{1} + c_{2} - c_{3} + \dots + (- 1)^{r} c_{r} = (- 1)^{r} \frac{( n - 1 )!}{r ! ( n - r - 1 )!}$ .

~15 minProof · checked by AIBinomial TheoremCoefficient Extraction

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIV. Binomial Theorem: Any Index, Examples XIV.c, No. 18 (part 1)

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