Determine whether the series # sum_(n=1)^oo (2n^2 +3n)/sqrt(5+n^5)# is convergent or divergent. How do i tell which comparison test to use?
1 Answer
The series:
is divergent.
Explanation:
We need to determine the convergence of the series:
We can see that the numerator is of order
For
is convergent only for
To demonstrate this formally, consider the series:
as stated above this series is divergent based on the p-series test.
Now evaluate the limit:
As the limit exists and is finite, based on the limit comparison test also the first series is divergent.