An algebra problem by Rahil Sehgal

Algebra Level 4

\[\sum_{i=4}^{8} \dfrac{i^8 + 24i^7 + 28i^6 -240i^5-129i^4+1280i^3+32i^2-672i+576}{i^{10}+4i^9-22i^8-80i^7+161i^6+460i^5-428i^4-672i^3+576i^2} \]

Find the value of the above expression to about 3 decimal places.

Inspiration

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