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

question 277

Multiple Choice

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

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

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Definitions:

Tonometry

A diagnostic test to measure the pressure inside the eye, used primarily in screening and monitoring for glaucoma.

Nyctalopia

Night blindness, a condition making it difficult or impossible to see in low light or darkness.

Nyctal

Relating to the night; often used in the context of nyctalopia, or night blindness.

Radial Keratotomy

A surgical procedure to correct myopia (nearsightedness) by making radial incisions in the cornea to flatten it.