The discussion revolves around determining the convergence or divergence of the series (∞,n=1) ∑ (n² - 1)/(3n⁴ + 1), which falls under the topic of series convergence tests in calculus.
The discussion is ongoing, with participants exploring the limit of the ratio of terms and questioning the validity of their approaches. Some guidance has been offered regarding the choice of the comparison series.
There is a focus on the limit as n approaches infinity, with participants expressing difficulty in reaching a conclusion about the series' behavior.
That's a reasonable choice.vande060 said:Homework Statement
determine whether the series diverges or converges
(∞,n=1) ∑ (n2 - 1)/(3n4 +1)
Homework Equations
The Attempt at a Solution
(∞,n=1) ∑ (n2 - 1)/(3n4 +1)
an = (n2 - 1)/(3n4 +1)
i thought bn should be n2/3n4 = 1/3n2
So what do you get when you take the limit?vande060 said:lim n-->∞ an/bn = (n2 - 1)/(3n4 +1) * 3n2
lim n-->∞ (3n4 - 3n2)/ (3n4 + 1)
not sure if this is going in the right direction here
Mark44 said:So what do you get when you take the limit?