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

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 $m+n$?