Solve the Problem $r$ Does the Infinite Series $1 + 3 r + 2 r ^ { 2 } + 3 r ^ { 3 } + r ^ { 4 } + 3 r ^ { 5 } + 2 r ^ { 6 } + 3 r ^ { 7 } + r ^ { 8 } + \ldots$

question 85

Multiple Choice

Solve the problem.
-For what value of $r$ does the infinite series $1 + 3 r + 2 r ^ { 2 } + 3 r ^ { 3 } + r ^ { 4 } + 3 r ^ { 5 } + 2 r ^ { 6 } + 3 r ^ { 7 } + r ^ { 8 } + \ldots$ converge?

• A) \(| r | < \frac { 3 } { 2 }\)
• B) \(| r | < \frac { 5 } { 2 }\)
• C) \(| r | < \frac { 2 } { 3 }\)
• D) \(| r | < 1\)

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