Question Number 68695 by fermat last updated on 15/Sep/19
![pour 1<k<n montrer que k(n+1−k)<(n+1/2)^2](https://www.tinkutara.com/question/Q68695.png)
$${pour}\:\mathrm{1}<{k}<{n}\:\:\:\:\:{montrer}\:{que} \\ $$$${k}\left({n}+\mathrm{1}−{k}\right)<\left({n}+\mathrm{1}/\mathrm{2}\right)^{\mathrm{2}} \\ $$
Answered by mind is power last updated on 15/Sep/19
![n+1−k<n+(1/2) k<n+(1/2) ⇒k(n+1−k)<(n+(1/2))^2](https://www.tinkutara.com/question/Q68804.png)
$${n}+\mathrm{1}−{k}<{n}+\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${k}<{n}+\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow{k}\left({n}+\mathrm{1}−{k}\right)<\left({n}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \\ $$