Series of Circles inscribed in an equilateral Triangle

This is a problem from a discrete set I'm working on, and I could use a little help.

the question reads as follows.

An equilateral triangle has each side length 1000. In this triangle, a circle is inscribed. Then in the space remaining on each corner, incribe another circle. The second set of circles touch two sides of the triangle and the edge of the previous circle. Keep proceeding in this manner, making smaller and smaller circles that approach the vertices of the triangle.

**What i really want to know is some sort of formula to find the radii of each of the circles.**

thanks a ton in advance guys