00:01
So in order for us to determine whether this series will converge or diverge or not, since we have it in this like recursive form, it might be a good idea to first just try to use the ratio test, especially since, remember when we do the ratio test, we have the limit as in -perch infinity of a -n plus 1 over a -n.
00:22
This is going to be equal to just, well, we already have a -n plus 1, and then we just leave a -n as a -n.
00:30
So this is going to be 1 plus natural log of n all over n times a n and then in denominator we just have a n so these a ns cancel out with each other and we would just be left with the limit as in approaches infinity of and i'm just going to go ahead and drop the absolute value since one plus natural log of in over in for large enough values of n is always positive this would be just one plus natural log of n over and now if we were to just trying to apply this limit directly, we would get infinity over infinity.
01:10
And normally when we have something like that, it's only hinting at us to apply lopatols.
01:15
So i'm going to write lh just to kind of represent we're applying lopatols here.
01:20
Not necessarily needed, but just kind of helps tell the reader what you're doing...