1/2 + 1/4 + 1/8 + 1/16 + · · ·

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 + · · ·


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