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Prove-that-x-2n-x-1-2n-2x-1-n-x-1-2-n-is-positive-integers-




Question Number 9527 by Joel575 last updated on 12/Dec/16
Prove that:  x^(2n)  ≥ (x−1)^(2n)  + (2x−1)^n   x ≥ (1/2),  n is positive integers
$$\mathrm{Prove}\:\mathrm{that}: \\ $$$${x}^{\mathrm{2}{n}} \:\geqslant\:\left({x}−\mathrm{1}\right)^{\mathrm{2}{n}} \:+\:\left(\mathrm{2}{x}−\mathrm{1}\right)^{{n}} \\ $$$${x}\:\geqslant\:\frac{\mathrm{1}}{\mathrm{2}},\:\:{n}\:\mathrm{is}\:\mathrm{positive}\:\mathrm{integers} \\ $$

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