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## Homework Statement

Use the limit comparison test to show the series converges or diverges: Sum from n=1 to infinity of ((5n^3)+1)/((2^n)((n^3)+n+1))

## Homework Equations

suppose Sum An and Sum Bn are two positive series. Let lim as n goes to infinity of An/Bn = c: 1) if 0<c<inifinity then either both converge or both diverge; 2) if c=0 and Sum Bn converges, so does Sum An; 3) if c=infinity and Sum Bn diverges, so does Sum An

## The Attempt at a Solution

See attached - series An is very complex. I'm not sure it goes to infinity like I assumed, nor am I sure that I picked an appropriate Bn equation. Please help thanks.