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Spain Mathematical Olympiad
1984 Spain Mathematical Olympiad
4
limit of product of cos\frac{x}{2^k} from k=1 to n
limit of product of cos\frac{x}{2^k} from k=1 to n
Source: Spanish Mathematical Olympiad 1984 P4
August 2, 2018
trigonometry
Product
geometry
Problem Statement
Evaluate
lim
n
→
∞
c
o
s
x
2
c
o
s
x
2
2
c
o
s
x
2
3
.
.
.
c
o
s
x
2
n
\lim_{n\to \infty} cos\frac{x}{2}cos\frac{x}{2^2} cos\frac{x}{2^3}...cos\frac{x}{2^n}
lim
n
→
∞
cos
2
x
cos
2
2
x
cos
2
3
x
...
cos
2
n
x
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