Adding 4 copies of 1 − 2 + 3 − 4 + · · ·, using only shifts and term-by-term addition, yields 1.
Only the first four terms of the series are shown. A white disk represents +1; a reddish disk represents −1. The units are grouped on top of each other as they occur within the terms of the series. A black line indicates a plus/minus pair, which annihilate to 0. An intermediate reduction to two copies of 1 − 1 + 1 − 1 + · · · is visible in the top row. The result of the addition is a single positive unit, highlighted in green at the upper left.
{{vector version available|Pm1234 linearity.svg}} == Summary == Adding 4 copies of 1 − 2 + 3 − 4 + · · ·, using only shifts and term-by-term addition, yields 1. Only the first four terms of the series are shown.