Ferocious Series?

Algebra Level 2

\[ \frac {\color{red}{3}} {\color{purple}{4}} + \frac {\color{red}{5}} {\color{purple}{36}} + \frac { \color{red}{7} } {\color{purple}{144}} + \frac {\color{red}{9}}{\color{purple}{400}} + \frac {\color{red}{11}}{\color{purple}{900}} + \ldots = \ ? \]

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