9709 P11 - Nov 2020 - Q8 - 7 marks
884
A geometric progression has first term \(a\), ratio \(r\), and sum to infinity \(S\). A second has first term \(a\), ratio \(R\), and sum to infinity \(2S\).
(a) Show that \(r=2R-1\). [3]
The third term of the first equals the second term of the second.
(b) Express \(S\) in terms of \(a\). [4]
