Sumerian/Babylonian proof of Pythagoras' theorem based on summation of infinite geometric series

An ancient Sumerian/Babylonian cuneiform clay tablet contains an image consisting of a right triangle subdivided into a sequence of similar right triangles, having the same common ratio between the sizes of the successive sub-triangles. Summing the lengths of the edges along each of these, using the standard formula for the sum of a geometrical series, and equating this to the corresponding edge length of the original triangle implies Pythagoras' theorem. Of course, the tablet does not contain any such detailed explanation, and it is questionable whether the formula for the sum of an infinite geometrical series would have been known to the Sumerians/Babylonians. But interpreting the image on the cuneiform tablet in this way provides a candidate for the oldest possible proof of the Pythagoras theorem.