💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

JH
Numerade Educator

Like

Report

Problem 29 Easy Difficulty

Use the Root Test to determine whether the series is convergent or divergent.
$ \displaystyle \sum_{n = 1}^{\infty} \left ( 1 + \frac {1}{n} \right)^{n2} $

Answer

Divergent

Discussion

You must be signed in to discuss.

Video Transcript

but use the rue test to determine whether the Siri's converges. So in the exponents there that should be and square. So are they. In is one plus one over n and square. And so now you use the root test, which requires that you look at the limit and goes to infinity and we'LL take the absolute value of Anne and then we take the end room of this. So this is the thing that we take the limits off. I can drop the absolute value because our man is positive. So here's my Anne. And then I'm raising that to the one over an hour. And now recall this fax from algebra. If you'd taken exponents and raise it to another exponents, you just multiplied into exponents. So in our case, we could just multiply these two, and that gives us an end. So we have a limit and goes to infinity one plus one over and to the end power and by definition, we'LL have to go back to the first half of the book. But the number he was defined as this limit and we know that the number he is bigger than one. So we conclude that the Siri's diverges by the root test