00:01
In this problem, we have to determine the convergence or divergence of the series.
00:07
And specifically, we have to determine the test to use.
00:11
We're not told the test to use.
00:13
So let's first start out with what we're given.
00:16
We're given the series from n equals 1 to infinity of the square root of n to the 4th plus 1, all over n cubed plus n.
00:25
Well, in this case, we can use the limit comparison test, and we can compare it with b sub n equals 1 over n.
00:32
Now, why are we using 1 over n? well, we know the convergence or divergence of the series of 1 over n.
00:40
That's known.
00:41
We can use that to compare the convergence or divergence of the series we're given.
00:49
So we can take the limit as n approaches infinity of a sub n over b sub n.
00:55
A sub n is what we're given, and b sub n is what we're comparing it to.
00:58
So we'll have the limit as n approach is infinity of the square root of n to the fourth plus 1 all over n cubed plus n.
01:08
Then we'll divide that whole quantity by 1 over n...