examday

/TMUA

A square of side length 2 units contains a circle of radius $R_1$ that is internally tangential to the square. A second smaller circle of radius $R_2$ is inscribed in a corner of the square and is tangential to the circle and the square. Another circle of radius $R_3$ is inscribed in the same corner and is tangential to the smaller circle (radius $R_2$) and the square, and so on ad infinitum for radii $R_4,R_5$, etc.

Find $\displaystyle\sum_{t=1}^\infty R_t$.