E-TG01 · A square leaves two sign branches
The numbers \(2\), \(4\cos x\), \(\displaystyle \frac{1}{2}\) form a GP, where \(0\le x<2\pi\).
Show that \(\displaystyle \cos^{2} x= \frac{1}{16}\), and express r in terms of x.
Let \(\displaystyle \alpha = \cos^{- 1} (\frac{1}{4})\). List all x and match each to its ratio.
Find the sum to infinity for each resulting progression, stating why each sum exists.
Complete-answer checking, worked solutions and indicative written criteria.
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