Question Number 68695 by fermat last updated on 15/Sep/19
$${pour}\:\mathrm{1}<{k}<{n}\:\:\:\:\:{montrer}\:{que} \\ $$ $${k}\left({n}+\mathrm{1}−{k}\right)<\left({n}+\mathrm{1}/\mathrm{2}\right)^{\mathrm{2}} \\ $$
Answered by mind is power last updated on 15/Sep/19
$${n}+\mathrm{1}−{k}<{n}+\frac{\mathrm{1}}{\mathrm{2}} \\ $$ $${k}<{n}+\frac{\mathrm{1}}{\mathrm{2}} \\ $$ $$\Rightarrow{k}\left({n}+\mathrm{1}−{k}\right)<\left({n}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \\ $$