Trignometry+Summation

Calculus Level 5

The sum \( \displaystyle \sum _{ n=1 }^{ 50 }{ \tan ^{ -1 }{ \left( \frac { 2n }{ { n }^{ 4 }-{ n }^{ 2 }+1 } \right) } } \) can be expressed as \( \tan^{-1} k \).
Find the value of \(k\).

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