Answer the following questions related to infinite geometric series.
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
Answer the following questions related to infinite geometric series.
(i) State the condition on the common ratio r under which the infinite series a+ar+ar2+ar3+⋯ converges.
(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.
(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.