For What Values of X Does the Series Converge Absolutely $$\sum _ { \mathrm { n } = 0 } ^ { \infty } ( - 1 ) ^ { \mathrm { n } } ( 9 \mathrm { x } + 5 ) ^ { \mathrm { n } }$$

question 115

Multiple Choice

For what values of x does the series converge absolutely?
- $$\sum _ { \mathrm { n } = 0 } ^ { \infty } ( - 1 ) ^ { \mathrm { n } } ( 9 \mathrm { x } + 5 ) ^ { \mathrm { n } }$$

• A) \(- 2 \leq x < - \frac { 8 } { 5 }\)
• B) \(- \frac { 2 } { 3 } < x \leq - \frac { 4 } { 9 }\)
• C) \(- 2 < x < - \frac { 8 } { 5 }\)
• D) \(- \frac { 2 } { 3 } < x < - \frac { 4 } { 9 }\)

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Definitions:

Weber's Law

A principle in psychophysics stating that the smallest change in a stimulus that can be detected is a constant proportion of the baseline stimulus.

Noticeable Difference

The smallest change in a stimulus that can be detected by the senses.

Minimum Change

The least alteration that can occur in a situation or in the value of a variable.

Absolute Threshold

The minimum intensity of a stimulus at which it can be detected by an individual at least 50% of the time.