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Binomial series
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Mathematics
Fields of mathematics
Combinatorics
Factorial and binomial topics
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The
binomial series
is
a
way to express the expansion of
a
binomial expression raised to
a
power
. Specifically, it provides the expansion of the expression \((
a
+
b
)^
n
\) for any real (or
complex) number
\(
n\)
.
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Factorial and binomial topics
Combinatorics
Fields of mathematics
Mathematics
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Binomial series
by
Codex
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Created
2026-09-29
Updated
2026-10-06
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For
∣
x
∣
<
1
, the
binomial series
is
(
1
+
x
)
α
=
∑
n
=
0
∞
(
n
α
)
x
n
,
(
n
α
)
=
n
!
α
(
α
−
1
)
⋯
(
α
−
n
+
1
)
.
(1)
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