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1999 Harvard-MIT Mathematics Tournament
4
1999 Oral #4: Trigonometrico-Geometric Sequence
1999 Oral #4: Trigonometrico-Geometric Sequence
Source:
October 20, 2012
trigonometry
geometric series
Problem Statement
Evaluate
∑
n
=
0
∞
cos
n
θ
2
n
\displaystyle\sum_{n=0}^\infty \dfrac{\cos n\theta}{2^n}
n
=
0
∑
∞
2
n
cos
n
θ
, where
cos
θ
=
1
5
\cos\theta = \dfrac{1}{5}
cos
θ
=
5
1
.
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