A geometric progression G has positive first term a, common ratio r (where 0< r < 1 ) and sum to infinity S. The sum to infinity of even-numbered terms of G, i.e. 2nd, 4th, 6th...terms is ((-1/2)S).
i)Find the value of r
ii) Given that the third term of G is 2, find that the sum to infinity of the odd-numbered terms of G i.e. 1st, 3rd, 5th... terms.
Thanks!