High Quality Content by WIKIPEDIA articles! In mathematics, the infinite series 1/4 + 1/16 + 1/64 + 1/256 + · · · is an example of one of the first infinite series to be summed in the history of mathematics; it was used by Archimedes circa 250–200 BC. Its sum is 1/3. More generally, for any a, the infinite geometric series whose first term is a and whose common ratio is 1/4 is convergent with the sum