The first problem looks good to me, and you have the right idea for the second. What do you get when you try to take the -th root?
Good morning All,
I am working on ratio and root tests for infinite series. I would like to post what I have done, and see if anyone agrees with it. Please see below:
By the Ratio Test...
And...
Therefore...
The orignal series is Absolutely Convergent.
Are we good here?
My second problem is:
I'm not really sure where to start here. Would I apply the root test to this problem?
Thanks!
When I try to take the nth root i get the following:
That can't be right??? I have three problems; one is supposed to be divergent, one conditionally convergent, and one absolutely convergent. Since my first problem was absolutely convergent (and I was able to follow the entire process for the first problem) I would have thought that the second problem would be either conditonally convergent or divergent.
...so, where did I go wrong?
Ok, I am waiting to hear back with respect to whether or not using the alternating series test is acceptable.
In the interim, I have worked out the last of three problems and concluded that:
By Ratio Test...
Therefore...
By the Ratio test, the series Diverges
So, this leaves me with my remaining series that is conditionally convergent. And, this means that if I am able to use the Ratio or Root Test, I should wind up with a limit equal to one... right?
Plato,
I am noticing a trend with the lesson plans that I am following; the questions seem to be quite difficult using the methods covered in that section, but following section will introduce a method that makes the problem quite simple to do. I assume this one is the same.
I am not a huge fan of the way the text book is organized, but i am nearly done with it so it's not worth complaining now.
I appreciate your patience. I used to tutor physics in college, so I know it can be trying when someone keeps mising the fundamental ideas. Thank you for continuing to work with me.
Please correct me if I am out of whack here...
Let
So...
By Alternating Series Test... Convergent
Let A Divergent P-series
So...
By Limit Comparison Test... Divergent
This doesn't make sense, does it?
Would it make ore sense if the order of the tests was reversed?