Summation vs Radicals

Algebra Level 4

k=12011+(1+1k)2+1+(11k)2= ?\large\displaystyle\sum_{k=1}^{20}\frac1{\sqrt{1+\left(1+\frac{1}{k}\right)^2}+\sqrt{1+\left(1-\frac{1}{k}\right)^2}}=\ ?

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