Chase the limit!

Calculus Level 3

Let \(f(n) = 1+4+11+24+45+76+\ldots+\frac{n^3+2n}3\). Evaluate

\[ \lim _{ n\rightarrow \infty } { \frac { 24 f(n) } { { n }^{ 4 } } } .\]

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