Question

use the limit comparison test

Answer 1

\[\sum_{n=1}^{\infty} (5n ^{3}+1)\div(2^{n}(n ^{3}+n+1))\]

Answer 2

since \(n^3+n+1<n^3+1\) you can compare to
\[\frac{5n^3+1}{2^n(n^3+1)}\]

Answer 3

or if you prefer
\[\frac{5}{n^n}\]

Answer 4

oops
\[\frac{5}{2^n}\]

Answer 5

ok so then where do i go from \[(n ^{3}+1)\div(n ^{3}+n+1)\]