#1429 · Algebra · Linear equations

Binomial coefficient sum relation

If $c_0, c_1, c_2,
ot_dots, c_n $d e n o t e t h ecoe f f i c i e n t s in t h ee x p an s i o n o f$ (1+x)^n $, p r o v e t ha t$ \frac{c_1}{c_0} + \frac{2c_2}{c_1} + \frac{3c_3}{c_2} + \dots + \frac{nc_n}{c_{n-1}} = \frac{n(n+1)}{2}$.

~10 minProof · checked by AIBinomial TheoremCombinatorial Identities

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIII. Binomial Theorem: Positive Integral Index, Examples XIII.b, No. 19

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