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$\large a_n=\sqrt{ 1+\left(1+\dfrac{1}{n} \right)^2 }+\sqrt{ 1+\left(1-\dfrac{1}{n} \right)^2 }$

Consider a sequence $a_n$, $n\geq1$ as defined above. Compute $\dfrac{1}{a_1}+\dfrac{1}{a_2}+\cdots+\dfrac{1}{a_{20}}$.

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