limit comparison test

Question

Use the limit comparison test to determine whether the series which is the sum of the terms A_n=(5n^4-2n^2+3)/(2n^6-n+5) from n=1 to infinity converges or diverges.

Answer 1

(5n^4-2n^2+3)/(2n^6-n+5) <= 5n^4/2n^6=(5/2)n^-2=5/2n^2

p (our power) =2 p=2>1

hence the series converges via the p series test (p converges if greater than 1)