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Mathematics
Mathematics
Problem
Let
α
\alpha
α
be a 5th root of unity (
α
≠
1
\alpha \neq 1
α
=
1
), then the value of
α
[
1
+
∑
k
=
1
∞
α
k
(
1
−
α
)
(
1
−
α
2
)
…
(
1
−
α
k
)
]
\alpha \left[1 + \sum_{k=1}^{\infty} \alpha^k (1 - \alpha)(1 - \alpha^2) \dots (1 - \alpha^k)\right]
α
[
1
+
∑
k
=
1
∞
α
k
(
1
−
α
)
(
1
−
α
2
)
…
(
1
−
α
k
)
]
is
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