MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Harvard-MIT Mathematics Tournament
2014 Harvard-MIT Mathematics Tournament
31
2014 Guts #31: Sum of 2014th Powers of Cosines
2014 Guts #31: Sum of 2014th Powers of Cosines
Source:
August 26, 2014
trigonometry
ratio
complex numbers
geometric series
Problem Statement
Compute
∑
k
=
1
1007
(
cos
(
π
k
1007
)
)
2014
.
\sum_{k=1}^{1007}\left(\cos\left(\dfrac{\pi k}{1007}\right)\right)^{2014}.
k
=
1
∑
1007
(
cos
(
1007
πk
)
)
2014
.
Back to Problems
View on AoPS