Christmas Streak 05/88: Too Many Terms!

Algebra Level 4

\[ \frac{\displaystyle\ \ \ \sum_{k=1}^{399} \sqrt{20+\sqrt{k}}\ \ \ }{\displaystyle \sum_{k=1}^{399} \sqrt{20-\sqrt{k}}}\]

Find the value of the expression above to three decimal places.


This problem is a part of <Christmas Streak 2017> series.

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