Separation principle
In mathematics, the infinite series 1/2 + 1/4 + 1/8 + 1/16 + · · · is an elementary example of a geometric series that converges absolutely.
Its sum is
Direct proof
As with any infinite series, the infinite sum
is defined to mean the limit of the sum of the first Template:Mvar terms
as Template:Mvar approaches infinity. Multiplying Template:Mvar by 2 reveals a useful relationship:
Subtracting Template:Mvar from both sides,
As Template:Mvar approaches infinity, Template:Mvar tends to 1.
History
This series was used as a representation of one of Zeno's paradoxes.[1] The parts of the Eye of Horus were once thought to represent the first six summands of the series.[2]
See also
References
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- ↑ Description of Zeno's paradoxes
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
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