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JH
Numerade Educator

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Problem 4 Easy Difficulty

Test the series for convergence or divergence.
$ \frac {1}{\ln 3} - \frac {1}{\ln 4} + \frac {1}{\ln 5} - \frac {1}{\ln 6} + \frac {1}{\ln 7} - \cdot \cdot \cdot $

Answer

Converges

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Video Transcript

Let's test the Siri's for convergence or diversions. Well, we see that it's alternating, and here it looks like our bien should just be won over natural lava vent. So let's try the alternating Siri's test. So first of all, before we used the test, we have to ensure that the beings are positive. So check us for it. Now. We have two conditions. One we need. That's the limit of being a zero. So we have limit one over natural log that people to zero because the limit of natural long is infinity. One more condition. Here we need the n plus one to be less than or equal to B E n. Now in our keys, we need this and I could cross multiply that's equivalents of Ellen and less than or equal to ln ofhim plus one. And then you could exponentially ate both sides using the Basie and then use the fact that the E in the natural lager in verses and you end up with an equation. That's true. That must mean that this repression, this an apology here is true so that this is true, and therefore our answer is that it converges by and then here. Let's just abbreviate all straining Siri's test off, and now it's the finalist