limit comparison test

Question

Use the limit comparison test to determine whether the series which is the sum of the terms A_n=(5n⁴-2n²+3)/(2n⁶-n+5) from n=1 to infinity converges or diverges

Answer 1

I am not sure that Stanton D. is correct.

The SEQUENCE A_n clearly converges to 0.

The series also converges, but the reason is not so clear.

What is needed is a comparison series and that is a bit harder to come by.

1/n>A_n>1/n² and the limit comparison test doesn't work here since both A_n and i/n² have limit 0.

What can be shown is that 3/n^2 is greater than A_n for all n and that gives the necessary comparison.