does the series converge or diverge show work sigman1 infini

Solution

sigma(n=1, infinity) (n^3+5n+1) / (n^3+4n^2)

as n tends to infinity

(1 + 5/n^2 + 1/n^3 ) / (1 + 4/n)

= 1

and denominaotr is dominating than numerator

thus series converges.