How do you use the integral test to determine if # sum_(n=3)^(oo) 1/(nlnnln(lnn))# is convergent or divergent?
This sum diverges.
For a series:
If the integral
is finite then the series will converge.
we will have the integral:
Consider the substitution:
Which will give us (bu the chain rule):
We also have that:
So the integral now becomes:
So evaluating these limits will give:
So the integral does not have a finite values hence the sum diverges.