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1 + 2 + 4 + 8 + ⋯
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Mathematics
Fields of mathematics
Arithmetic
Binary arithmetic
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The
series
\(
1
+
2
+
4
+
8
+ \ldots\) is
a
geometric series
where the
first
term \(
a
=
1
\) and the common
ratio
\(
r
=
2\)
. The sum of an infinite
geometric series
can be calculated using the
formula
: \[
S
= \frac{
a
}{
1
-
r
} \] This
formula
is valid only for \(|
r
| <
1\)
.
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Binary arithmetic
Arithmetic
Fields of mathematics
Mathematics
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