Prove-that-no-three-consecutive-binomial-coefficient-can-be-in-G-P-or-H-P-

Question Number 22423 by Tinkutara last updated on 17/Oct/17

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{no}\:\mathrm{three}\:\mathrm{consecutive} \\ $$$$\mathrm{binomial}\:\mathrm{coefficient}\:\mathrm{can}\:\mathrm{be}\:\mathrm{in}\:\mathrm{G}.\mathrm{P}.\:\mathrm{or}\:\mathrm{H}.\mathrm{P}. \\ $$

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