1-8

In mathematics, the infinite series 1/2 + 1/4 + 1/8 + 1/16 + ··· is an elementary example of a geometric series that converges absolutely.
There are many different expressions that can be shown to be equivalent to the problem, such as the form: 2−1 + 2−2 + 2−3 + ...
The sum of this series can be denoted in summation notation as:






1
2


+


1
4


+


1
8


+


1
16


+
⋯
=

∑

n
=
1


∞




(


1
2


)


n


=



1
2


1
−


1
2





=
1.


{\displaystyle {\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}+\cdots =\sum _{n=1}^{\infty }\left({\frac {1}{2}}\right)^{n}={\frac {\frac {1}{2}}{1-{\frac {1}{2}}}}=1.}

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