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Numerade Educator



Problem 29 Easy Difficulty

Determine whether the series is convergent or divergent. If it is convergent, find its sum.
$ \displaystyle \sum_{n = 1}^{\infty} \frac {2 + n}{1 - 2n} $


$$-\frac{1}{2} \neq 0$$


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Video Transcript

Let's determine whether or not the following Syriza's conversion or diversion. If it's convergent, let's go ahead and find some. So looking at this, Siri's here. Let's just focus on the terms that are being added. Usually, the book will denote this by the end. Well, here we can use the with called the Test for Divergence. And in our case, here's the statement. If the limit of a M does not exist or if the limit does exist but equal zero, then the Siri's will diverge. And again, it doesn't matter what your starting point is. It could be any number here instead of one. So on our problem. Let's go ahead and see if we could use this test here. So let's take the limit of an hoops limit as n goes to infinity of a end, that equals limit and goes to infinity two plus and over one minus to end that here, if you like, you could divide top and bottom by N and you have two over and plus one in the numerator, one over and minus two in the denominator. And as we take that limit, thes terms go to zero. But you still have a one on top and negative two on the bottom. That's negative one half, so the limit does exist, but it's not zero. Therefore, this will diverge, diverges and you could even say why Bye, the test for divergence and that's your final answer.