How do you test the series #Sigma 1/(ln(n!))# from n is #[2,oo)# for convergence?
Given the series:
First we note that for
We can now analyse the convergence of the series:
which is easier to determine using the integral test.
We take as test function:
all the hypothes of the integral test are satisfied and the series (2) is convergent only if the integral:
is also convergent.
Now we have:
So the series (2) is divergent and then also the series (1) is divergent.