Induction problem

Given n positive numbers $x_1, x_2, x_3, ... x_n$ such that

$$x_1+x_2+x_3+\dots +x_n \leq \frac{1}{3}.$$
Prove by induction that $$(1-x_1)(1-x_2)(1-x_3)....(1-x_n) \geq \frac{2}{3}.$$


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Erdos Erdos
  • Erdos Erdos

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