Question Number 32277 by abdo imad last updated on 22/Mar/18
![for x_i ∈[0,1] prove that (1−x_1 )(1−x_2 )....(1−x_n ) ≥1−(x_1 +x_2 +.... +x_n ).](https://www.tinkutara.com/question/Q32277.png)
$${for}\:{x}_{{i}} \:\in\left[\mathrm{0},\mathrm{1}\right]\:{prove}\:{that} \\ $$$$\left(\mathrm{1}−{x}_{\mathrm{1}} \right)\left(\mathrm{1}−{x}_{\mathrm{2}} \right)….\left(\mathrm{1}−{x}_{{n}} \right)\:\geqslant\mathrm{1}−\left({x}_{\mathrm{1}} +{x}_{\mathrm{2}} \:+….\:+{x}_{{n}} \right). \\ $$