How do you use the integral test to determine if #Sigma lnn/n^2# from #[1,oo)# is convergent or divergent?
1 Answer
The series:
Explanation:
If we use:
as test function, we have that for
# f(x) # is positive
# lim_(x->oo) f(x) = 0 #
#f(n) = lnn/n^2#
Calculating the first derivative:
we can also see that
so all the hypotheses of the integral test theorem are satisfied and the series is convergent if the integral:
also converges.
Let's calculate the indefinite integral by parts:
So:
That is the integral is convergent and so is the series.