单词	Bernoulli Inequality
释义	Bernoulli Inequality (1) where , . This inequality can be proven by taking a Maclaurin Seriesof , (2) Since the series terminates after a finite number of terms for Integral , the Bernoulli inequalityfor is obtained by truncating after the first-order term. When , slightly more finesse is needed. In thiscase, let so that , and take (3) Since each Power of multiplies by a number and since the Absolute Value of the Coefficient ofeach subsequent term is smaller than the last, it follows that the sum of the third order and subsequent terms is a Positivenumber. Therefore, (4) or (5) completing the proof of the Inequality over all ranges of parameters.
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