Seriously serrated series

Algebra Level 3

1+112+122+1+122+132+1+132+142++1+120192+120202=?\sqrt{ 1+ \dfrac{1}{1^2} + \dfrac{1}{2^2} } + \sqrt{ 1+ \dfrac{1}{2^2} + \dfrac{1}{3^2} } + \sqrt{ 1+ \dfrac{1}{3^2} + \dfrac{1}{4^2} }+\cdots+\sqrt{ 1+ \dfrac{1}{2019^2} + \dfrac{1}{2020^2} } = ?

Obviously not original, but modified for 2020.

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