Telescope Summation

Algebra Level 4

\[ \sum_{n=1}^{20} \dfrac{8n}{4n^4+1}= \dfrac85 + \dfrac{16}{65} + \dfrac{24}{325} + \cdots + \dfrac{160}{640001} \]

Let \(x\) denote the value of the summation above. Find \(841x\).

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