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JH
Numerade Educator

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Problem 5 Easy Difficulty

Test the series for convergence or divergence.
$ \displaystyle \sum_{n = 1}^{\infty} \frac {(-1)^{n - 1}}{3 + 5n} $

Answer

CONVERGES

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Video Transcript

let's test the Siri's for convergence or diversions. So first thing I notice here is that this thing is alternating due to this minus do basically here. And just because the numerator hopes we have this negative one to the end minus one power. So the first thing that comes to mind often when alternating Siri's is the alternating Siri's test. So here our BN is one over three plus five in so basically everything in the A n except the negative one to the exponents. So this is positive. That's good. That's one condition. The second condition is that we need the limit of Beyonce and be zero as n goes to infinity and I will be true here. The numerator is just one, but the denominator goes to infinity. So this limit is just zero. And then finally for part three, the last condition we need bien plus one less than or equal to be in for all. And so in this case and peoples one, two and so on because that's the starting point for him. So this is true because one over three plus five and then in plus one. So this is the left hand side, and then the right hand side is just one over three plus five in. This is true because the denominator denominator I'm left is larger. So we were satisfying all the conditions for the alternate theories test. Therefore, the Siri's converges Bye, the alternating Siri's test, and that's your final answer.