# Why does the integral test not apply to #Sigma (-1)^n/n# from #[1,oo)#?

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The integral test requires the function being integrated to be continuous, positive, and decreasing. The function ( \frac{(-1)^n}{n} ) oscillates in sign, so it fails to meet the criteria of being positive and decreasing. Therefore, the integral test cannot be applied to the series ( \sum_{n=1}^\infty \frac{(-1)^n}{n} ).

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