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 $$(1-x_1)(1-x_2)(1-x_3)....(1-x_n) \geq \frac{2}{3}.$$

Answer

Answers can only be viewed under the following conditions:
  1. The questioner was satisfied with and accepted the answer, or
  2. The answer was evaluated as being 100% correct by the judge.
View the answer
Erdos Erdos
4.7K
  • Erdos Erdos
    0

    Please leave a comment if you need any clarifications.

The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to a 50% commission on every question that your affiliated users ask or answer.