Problem:
If ∑n=0∞cos2nθ=5, what is the value of cos2θ ?
Answer Choices:
A. 51
B. 52
C. 55
D. 53
E. 54
Solution:
The given series is geometric with an initial term of 1 and a common ratio of cos2θ, so its sum is
5=n=0∑∞cos2nθ=1cos2θ1=sin2θ1
Therefore sin2θ=51, and
cos2θ=12sin2θ=152=53
The problems on this page are the property of the MAA's American Mathematics Competitions