Consider a geometric progression whose first term is and common ratio
MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
Consider a geometric progression whose first term is a and common ratio r. Its partial sum after n terms is denoted by Sn.
(i) Explain, with suitable algebraic reasoning, what happens to Sn as n→∞ when ∣r∣<1.
(ii) Give one numerical illustration to support your answer in part (i).
(iii) State clearly why a similar limiting sum does not exist when r≥1 or r≤−1, pointing out the essential difference in behaviour of the terms of the progression in these cases.