In Calculus, what is the purpose of figuring out if the series converges or diverges?


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John McCann answered





How quickly the convergent function approaches the x axis is important, generally, if you wish to take a finite area under the curve. Though both functions never touch the x axis the convergent function comes as close as is possible quickly and it's area under the curve is measurable. The divergent function has an infinite area as it approaches the x axis too slowly to have the area under the curve be measurable.

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