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Proposition: Generalized Bernoulli's Inequality

Let $x_1,\ldots,x_n$ be non-negative real numbers for some natural number $n\in\mathbb N.$ Then the following inequality holds:

$$\prod_{k=1}^n(1+x_k)\ge 1+\sum_{k=1}^n x_k.$$

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Proofs: 1

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References

Bibliography

  1. Modler, F.; Kreh, M.: "Tutorium Analysis 1 und Lineare Algebra 1", Springer Spektrum, 2018, 4th Edition