#1427 · Algebra · Sequences & series

Sum of Weighted Coefficients I

If $c_{0}, c_{1}, c_{2}, \dots, c_{n}$ denote the coefficients in the expansion of $(1 + x)^{n}$ , prove that $c_{1} + 2 c_{2} + 3 c_{3} + \dots + n c_{n} = n 2^{n - 1}$ .

~5 minProof · checked by AIBinomial TheoremSummation

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIII. Binomial Theorem: Positive Integral Index, Examples XIII.b, No. 17

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