E-TG04 · Convergence changes with a scale parameter
A GP has first term 1 and common ratio \(k\cos x\), where \(k>0\) and \(0\le x\le\pi\).
State the condition for convergence in terms of k and x.
Give the complete set of x for each case: \(0<k<1\), \(k=1\), and \(k>1\).
For \(\displaystyle k=2\), find x if the sum to infinity is 2. Check that x is admissible.
Complete-answer checking, worked solutions and indicative written criteria.
Open the complete answer form