Simplify Each Of These Fractions First!

Algebra Level 3

\[\dfrac 1{1+1^2 + 1^4} + \dfrac 2{1+2^2 + 2^4} + \dfrac 3{1+3^2 + 3^4} +\cdots + \dfrac {99}{1+99^2 + 99^4} \]

The value of the expression above lies between which of the following pairs of numbers?

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