Mathematics

Problem

Two infinite series are defined as follows: Series A:

\displaystyle S_A = \sum_{n=0}^{\infty} 5\bigl(0.6\bigr)^{n}

Series B:

\displaystyle S_B = \sum_{n=1}^{\infty} 8\bigl(0.4\bigr)^{\,n-1}

A student wants to know which series has the greater sum and by how much. a. Evaluate

S_A

and

S_B

exactly. b. Indicate which series has the greater sum and calculate the exact difference

|S_A-S_B|

. c. Interpret your numerical comparison: explain, in one or two sentences, what the result implies about the long-term total value contributed by each series.

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