Solve the Problem $1 + 6 r + r ^ { 2 } + 6 r ^ { 3 } + r ^ { 4 } + 6 r ^ { 5 } + r ^ { 6 } + \ldots$

question 296

Multiple Choice

Solve the problem.
-Find the sum of the infinite series $1 + 6 r + r ^ { 2 } + 6 r ^ { 3 } + r ^ { 4 } + 6 r ^ { 5 } + r ^ { 6 } + \ldots$ for those values of $r$ for which it converges.

• A) \(\frac { 1 + 6 r } { 1 + r ^ { 2 } }\)
• B) \(\frac { 1 - 6 r } { 1 + r ^ { 2 } }\)
• C) \(\frac { 1 - 6 r } { 1 - r ^ { 2 } }\)
• D) \(\frac { 1 + 6 r } { 1 - r ^ { 2 } }\)

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