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# 9: Sequences and the Binomial Theorem

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Thumbnail: The sum of the areas of the rectangles is greater than the area between the curve $$\displaystyle f(x)=1/x$$ and the $$\displaystyle x$$-axis for $$\displaystyle x≥1$$. Since the area bounded by the curve is infinite (as calculated by an improper integral), the sum of the areas of the rectangles is also infinite.