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Putnam
1949 Putnam
A6
Putnam 1949 A6
Putnam 1949 A6
Source: Putnam 1949
March 20, 2022
Putnam
trigonometry
Problem Statement
Prove that for every real or complex
x
x
x
∏
k
=
1
∞
1
+
2
cos
2
x
3
k
3
=
sin
x
x
.
\prod_{k=1}^{\infty} \frac{1+2\cos \frac{2x}{3^{k}}}{3} =\frac{\sin x}{x}.
k
=
1
∏
∞
3
1
+
2
cos
3
k
2
x
=
x
sin
x
.
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