#1430 · Algebra · Linear equations

Product of adjacent binomial coefficients

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 $, p r o v e t ha t$ (c_0 + c_1)(c_1 + c_2) \dots (c_{n-1} + c_n) = \frac{c_1 c_2 \dots c_n (n+1)^n}{n!}$.

~15 minProof · checked by AIBinomial TheoremAlgebraic Manipulation

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIII. Binomial Theorem: Positive Integral Index, Examples XIII.b, No. 20

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