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2022 JHMT HS
10
Maximum Value of Infinite Sum
Maximum Value of Infinite Sum
Source:
August 9, 2024
calculus
trigonometry
2022
Problem Statement
The maximum value of
2
∑
n
=
1
∞
sin
(
n
θ
)
4
4
n
2\sum_{n=1}^{\infty} \frac{\sin(n\theta)}{44^n}
2
n
=
1
∑
∞
4
4
n
sin
(
n
θ
)
over all real numbers
θ
\theta
θ
can be expressed as a common fraction
p
q
\tfrac{p}{q}
q
p
. Compute
p
+
q
p + q
p
+
q
.
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