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Numerade Educator



Problem 20 Easy Difficulty

Determine whether the series is convergent or divergent.
$ \displaystyle \sum_{n = 3}^{\infty} \frac {3n - 4}{n^2 - 2n} $




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Video Transcript

to demonstrate the Siri's, we will use several comparisons so three and minus for or and squared minus to end. It's going to be greater than three n minus for over just and minus two. Because when N is three or bigger, multiplying by and on the bottom will make the whole fraction smaller. And this, in turn, will be greater than three n minus four over end. Because since N is greater than minus two, Ah, and a larger denominator causes the fraction itself to be smaller. Well, this is equal to three end over end minus four over and which is three minus four over end. And in this case, we have a diversion Siri's because multiply or adding threes successively, infinitely many times we'LL go to infinity, whereas subtracting afore over n will eventually be subtracting or less zero. So this Siri's would be a diversion. And since our original Siri's is greater than that, we know by comparison test that if a N is greater than B and E and B n diverges than an also diverges. So in this case, are an it's what we started with our bien is what we found. So our Siri's is divergent