Two infinite series are defined as follows: Series A: Series B: A student wants to…
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
Two infinite series are defined as follows:
Series A: SA=n=0∑∞5(0.6)n
Series B: SB=n=1∑∞8(0.4)n−1
A student wants to know which series has the greater sum and by how much.
(1) Evaluate SA and SB exactly.
(2) Indicate which series has the greater sum and calculate the exact difference ∣SA−SB∣.
(3) Interpret your numerical comparison: explain, in one or two sentences, what the result implies about the long-term total value contributed by each series.