How do you use the limit comparison test to determine whether the following converge or diverge given #sin(1/(n^2))# from n = 1 to infinity?
1 Answer
Explanation:
The limit comparison test states that if
Let
Let's think about the end behaviour of
For large
We can use the small-angle approximation:
As
So, for large
Let
Then
This indeterminate result is discouraging, but we can apply L'Hôpital's rule:
If
Let
So,
But