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Numerade Educator



Problem 11 Easy Difficulty

Determine whether the series converges or diverges.
$ \displaystyle \sum_{k = 1}^{\infty} \frac { \sqrt [3]{k}}{\sqrt {k^3 + 4k + 3}} $




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Video Transcript

Okay. So people can t k thurman the Siri's. I'm gonna find the states because to a k on a case greater than on what then, Kay over cake. You plus four K plus three to the power of one third. And this is equivalent to one hour case square us for us three. Okay, Okay. And we know that case greater or equal to one. So this is square are people too. When you were his square past seven quarter thresher to our one third and stare. This is greater than when there were cases where past seven to the power of half Swear it one door keeper seven. And at last this is still greater than when you work in a cell. So for the last step, because so k square porcelain this world keeps you Oppa seven is less in her cell. We can square on both eyes. So there's going to be kissed there for seven. And this part this that is going to be a case where Class forty nine plus for ten k. So Yeah, so now we have the Siri's and we know that the timer is so now conclude that a k Siri's off a diver tous