MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - Other Middle and High School Contests
Math Prize For Girls Problems
2017 Math Prize for Girls Problems
20
Math Prize 2017 Problem 20
Math Prize 2017 Problem 20
Source:
September 27, 2017
Math Prize for Girls
Problem Statement
Compute the value of the sum
∑
k
=
1
11
sin
(
2
k
+
4
π
/
89
)
sin
(
2
k
π
/
89
)
.
\sum_{k = 1}^{11} \frac{\sin(2^{k + 4} \pi / 89)}{\sin(2^k \pi / 89)} \, .
k
=
1
∑
11
sin
(
2
k
π
/89
)
sin
(
2
k
+
4
π
/89
)
.
Back to Problems
View on AoPS