E-TA03 · A family with a zero-difference endpoint
The numbers \(\cos x\), \(k\), \(2-\cos x\) are consecutive terms of an AP, where \(0\le x<2\pi\).
Find k and express the common difference in terms of x.
Find all x for which the first five terms have sum \(\displaystyle \frac{25}{2}\).
Now allow x to vary again. Find the complete set of x for which every term of the infinite AP is strictly positive.
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