Infinite Cosine Series

Geometry Level 5

\[ \dfrac{\cos(\theta)}{5}+\dfrac{2\cos (2\theta)}{25}+\dfrac{3\cos (3\theta)}{125}+\dfrac{4\cos (4\theta)}{625}+\dfrac{5\cos (5\theta)}{3125}+\cdots \]

Let \(\theta\) be an acute angle with \(\cos\theta = \dfrac{7}{10}\). If the value of the series above can be expressed as \( \dfrac mn\), where \(m\) and \(n\) are coprime positive integers, find the value of \(m+n\).

×

Problem Loading...

Note Loading...

Set Loading...