# Simply Awsome!

Algebra Level 3

If,

$\sum _{ i=1 }^{ 200 }{ \sqrt { \left( 1+\frac { 1 }{ { i }^{ 2 } } +\frac { 1 }{ { \left( 1+i \right) }^{ 2 } } \right) } } =\frac { A }{ B }$

Find: $$A+B$$ where $$A$$ and $$B$$ are coprime positive integers.

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