Hundred Fractions is More Than Enough

Algebra Level 3

\[ \frac{2}{1} + \frac{2}{3} + \frac{4}{3} + \frac{4}{5} + \frac{6}{5} + \frac{6}{7} + \ldots + \text{ 100}^{\text{th}} \text{ term} \]

If the expression above is simplified to the closed form of \( \frac m n \) where \(m,n\) are coprime positive integers. What is the value of \(m+n\)?

Note - this problem is a part of the sets - 3's & 4's & QuEsTiOnS.
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