Consider the two infinite series A=3+1.5+0.75+0.375+⋯ and B=3+6+12+24+⋯.
a. (i) Find the common ratio of series A and of series B.
b. (ii) Decide, with reason, whether each series converges or diverges.
c. (iii) In not more than three sentences, explain how the magnitude of the common ratio determines the convergence or divergence of an infinite geometric series.