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ch11s3 - 11.3 The Integral Test and Estimates of Sums Its...

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11.3 The Integral Test and Estimates of Sums It’s possible to find the sum of a convergent geometric series or a series for which we can find a formula for the n th partial sum. Generally, it is difficult to find the exact sum of a convergent series. We will, however, be able to obtain a good estimate of the sum. We are going to begin to develop tests for convergence of a series. The first we are going to study is called the Integral Test. The Integral Test can only be used if the function representing the series is continuous, positive and decreasing for values greater than or equal to 1. Every test for convergence is not applicable to every type of series. Learning which test to use is important to your success in this chapter. We will use the Integral test when the function can be easily integrated. It involves the use of improper integrals. Integral Test Suppose f is a continuous, positive, decreasing function on and let a [1, ) n =f(n).
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