00:02
We have a sequence whose nth term is defined as natural log of n plus 1 divided by the square root of n.
00:11
And what we want to do is find if the sequence is convergent.
00:15
And if it does, we want to find what it's the limit is of that sequence.
00:20
Like what does the term become as n becomes infinite? so we're doing is take the limit as m becomes infinite of the natural log of n plus 1 over end of the one half.
00:33
I'm just going to rewrite as one half.
00:36
And if we let n become infinite, the numerator increases without bound, as is the denominator.
00:44
So it's in a determinant form, so we can use loquitals rule.
00:47
So that means we need to take the derivative of the numerator with respect to n and the denominator.
00:55
So the numerator, again, this is still under the limit.
01:01
The derivative of natural log is one over the argument that we multiplied by the derivative of the argument, but the derivative of the n is just one with respect to n...