#1532 · Algebra · Linear equations

Weighted Alternating Binomial Sum

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 $c_{0} - 2 c_{1} + 3 c_{2} - 4 c_{3} + \dots + (- 1)^{n} (n + 1) c_{n} = 0$ .

~15 minProof · checked by AIBinomial TheoremDifferentiation

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIV. Binomial Theorem: Any Index, Examples XIV.c, No. 18 (part 2)

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