How do you test the series #Sigma n/sqrt(n^3+1)# from n is #[0,oo)# for convergence?
The series diverges.
I would limit compare to
I come up with this by looking at dominant terms in the numerator and denominator of the nth term of the given series:
numerator: dominant term is
denominator: dominant term is
So the given series can be compared to
We know that
So we calculate
Since the limit is positive and finite and