Sum the series

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If the sum sqrt(1+ 1/1^2 + 1/2^2) + sqrt(1 + 1/2^2 + 1/3^2) + sqrt(1+ 1/3^2 + 1/4^2)+......+sqrt(1+ 1/1999^2 + 1/2000^2) equals to n - (1/n) where n E N. Then what is n/100?

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