1/2 + 1/4 + 1/8 + 1/16 + · · ·

In mathematics, the infinite series 1/2 + 1/4 + 1/8 + 1/16 + · · · is an elementary example of a series that converges absolutely.

It is a geometric series whose first term is 1/2 and whose common ratio is 1/2, so its sum is:$frac12+frac14+frac18+frac\{1\}\{16\}+cdots=frac\{1/2\}\{1-(+1/2)\}\; =\; 1.$

History

This series was used as a representation of one of Zeno's paradoxes. [ [http://web01.shu.edu/projects/reals/numser/series.html#zenonpdx Description of Zeno's paradoxes] ]

Binary

This infinite series is a representation of "0.111...₂", which is the binary equivalent of 0.999...₁₀, and which has many applications in educational research.

Notes

ee also

* 1/2 − 1/4 + 1/8 − 1/16 + · · ·