Let a+a r_{1}+a r_{1}^{2}+a r_{1}^{3}+\cdots and a+a r_{2}+a r_{2}^{2}+a r_{2}^{3}+\cdots be two different infinite geometric series of positive numbers with the same first term. The sum of the first series is r_{1}, and the sum of the second series is r_{2}. What is r_{1}+r_{2} ?
Answer Choices
A. 0
B. \dfrac{1}{2}
C. 1
D. \dfrac{1+\sqrt{5}}{2}
E. 2