MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
Consider the two infinite geometric series below.
Series P: 7,3.5,1.75,…
Series Q: 5,2,0.8,…
Answer the following questions.
(i) For each series, write the first term and the common ratio.
(ii) Decide whether each series converges and state the reason for your answer.
(iii) Without calculating exact numerical values of the sums, determine which series has the greater sum to infinity. Give a clear justification for your conclusion.