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Numerade Educator

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Problem 27 Easy Difficulty

Explain why the Integral Test can't be used to determine whether the series is convergent.
$ \displaystyle \sum_{n = 1}^{\infty} \frac {\cos \pi n}{\sqrt n} $

Answer

$a_{n}$ is not positive and decreasing

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Video Transcript

the key requirement for the integral test is that function must satisfy three conditions. It must be continuous. And that is to say when our function is agonize that term of the what? When you can a continuous function, we need a decreasing function and we need and always positive function. Coastline of Pai n is well, the very first term is negative. Since co sign of pi times one is co sign a pie which is negative one. So this function is not always going to be positive and therefore it fails. Thie condition for General Test