Answer the following questions related to infinite geometric series.
a. (i) State the condition on the common ratio r under which the infinite series a+ar+ar2+ar3+⋯ converges.
b. (ii) Explain, with reference to the limit of rn as n→∞, why the condition obtained in part (i) guarantees that the series has a finite sum.
c. (iii) Decide, with a brief reason in each case, whether the infinite series converges or diverges when the common ratio is
(a) r=0.8
(b) r=−0.6
(c) r=1.05.