(a)[3]
Show that $r = 2R - 1$.
(b)[4]
It is now stated that the 3rd term of the first progression equals the 2nd term of the second progression. Write $S$ in terms of $a$.
Mathematics 9709 · AS & A Level · Series
Series — practice question
A geometric progression starts with first term $a$, has common ratio $r$, and its sum to infinity is $S$. A different geometric progression also begins with first term $a$, but its common ratio is $R$ and its sum to infinity is $2S$.