#1428 · Algebra · Sequences & series

Sum of Weighted Coefficients II

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

~8 minProof · checked by AIBinomial TheoremIntegration

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIII. Binomial Theorem: Positive Integral Index, Examples XIII.b, No. 18

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