1/2 + 1/4 + 1/8 + 1/16 + ⋯

Common card · No. 435633

In mathematics, the infinite series ⁠1/2⁠ + ⁠1/4⁠ + ⁠1/8⁠ + ⁠1/16⁠ + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1. In summation notation, this may be expressed as 1 2 + 1 4 + 1 8 + 1 16 + ⋯ = ∑ n = 1 ∞ ( 1 2 ) n = 1. {\displaystyle {\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac...