Verified answer

good luck in your work since it diverges using a p-series

study to a million/n^2. if lim ((n^4 + 3n)/(5n^3 + 9)) / (a million / n^2) = p, then your sequence ought to converge (for the reason that all of us know that a million/n^2 converges). consequently: lim ((n^4 + 3n)/(5n^3 + 9)) / (a million / n^2) = lim [ (n^4+3n)*n^2 ] / [ 5n^3 + 9 ] = lim [ n^6 + 3n^3 ] / [ 5n^3 + 9] = lim [ a million + 3/n^3 ] / [ 5 / n^3 + 9 / n^6 ] -> divided via by skill of n^6. = infinity -> this reduces to (a million+0) / (some thing that is going to 0) = a million / (some thing small) = infinity. for the reason that infinity isn't bounded, all of us know that your sequence diverges.