The Cauchy-Schwarz inequality is considered one of the most important and widely used inequalities in mathematics....

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The Cauchy-Schwarz inequality is considered one of the most important and widely used inequalities in mathematics. This inequality states that Pigi i=1 k k ? Now, assume that the series n an with nonnegative terms a 0 is a convergent series. Use the Cauchy-Schwarz inequality and show that the series 1 an is convergent. n The Cauchy-Schwarz inequality is considered one of the most important and widely used inequalities in mathematics. This inequality states that Pigi i=1 k k ? Now, assume that the series n an with nonnegative terms a 0 is a convergent series. Use the Cauchy-Schwarz inequality and show that the series 1 an is convergent. n