How do i prove the positive term sequence x^x converges using Cauchy integral test ? I am not able to figure out how to integrate x^x ? Any ideas ?
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Originally Posted by pratique21 How do i prove the positive term sequence x^x converges using Cauchy integral test ? I am not able to figure out how to integrate x^x ? Any ideas ? Why should you need the integral test? Since it's a sequence, just evaluate . Obviously the sequence doesn't converge, and if it was a series and the terms don't go to 0, the series can't possibly converge either.
Just what happens when you hold back info ! The sequence I need to check for convergence is so i need a way to integrate it. And this one converges But how do i integrate it ?
Again, why should you need to integrate it? It's pretty obvious that it goes to .
Because that is necessary but not sufficient to prove convergence.
Originally Posted by pratique21 Because that is necessary but not sufficient to prove convergence. If it is a SEQUENCE then it is enough to show convergence by evaluating the limit of the terms to a number. If it is a SERIES then one must first show that the terms go to 0, and then apply some other test. Which is it?
umm...does series mean having a summation ? If yes, then it's a series.
Originally Posted by pratique21 umm...does series mean having a summation ? If yes, then it's a series. A sequence is a list of numbers following a pattern. A series is the sum of the numbers in the sequence. To show the series is convergent, you can use the ratio test. Since this ratio is less than 1, the series is convergent.
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