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Consider the p-series (\sum_{n=1}^{\infty}\frac{1}{n^{p}}) with (p>0). To apply the integral test, take the function (f(x)=\frac{1}{x^{p}}) for (x\ge 1). This function is positive, continuous, and decreasing on ([1,\infty)) for all (p>0), so the conditions of the integral test are satisfied. We _______ ___ ________ _____ ___ ___ ______ ______ ____ _____ __________ ______.
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