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Putnam
1952 Putnam
A5
Putnam 1952 A5
Putnam 1952 A5
Source:
May 29, 2022
Putnam
Problem Statement
Let
a
j
(
j
=
1
,
2
,
…
,
n
)
a_j (j = 1, 2, \ldots, n)
a
j
(
j
=
1
,
2
,
…
,
n
)
be entirely arbitrary numbers except that no one is equal to unity. Prove
a
1
+
∑
i
=
2
n
a
i
∏
j
=
1
i
−
1
(
1
−
a
j
)
=
1
−
∏
j
=
1
n
(
1
−
a
j
)
.
a_1 + \sum^n_{i=2} a_i \prod^{i-1}_{j=1} (1 - a_j) = 1 - \prod^n_{j=1} (1 - a_j).
a
1
+
i
=
2
∑
n
a
i
j
=
1
∏
i
−
1
(
1
−
a
j
)
=
1
−
j
=
1
∏
n
(
1
−
a
j
)
.
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