Find the Interval of Convergence Of $\sum _ { n = 0 } ^ { \infty } \frac { ( - 3 x ) ^ { n } } { 3 n + 1 }$

question 120

Multiple Choice

Find the interval of convergence of $\sum _ { n = 0 } ^ { \infty } \frac { ( - 3 x ) ^ { n } } { 3 n + 1 }$ .

• A) \(\left( - \frac { 1 } { 3 } , \frac { 1 } { 3 } \right)\)
• B) \(\left( - \frac { 1 } { 3 } , \frac { 1 } { 3 } \right]\)
• C) \(\left[ - \frac { 1 } { 3 } , \frac { 1 } { 3 } \right)\)
• D) \(\left[ - \frac { 1 } { 3 } , \frac { 1 } { 3 } \right]\)
• E) \(( - 3,3 )\)
• F) \(( - 3,3 ]\)
• G) \([ - 3,3 )\)
• H) \([ - 3,3 ]\)

---

Definitions:

A Priori Causal Theories

Preexisting theories, acquired from culture or factors that are particularly prominent in conscious attention at the moment.

Repress Unpleasant Information

The involuntary forgetting or pushing aside of difficult or disturbing facts, thoughts, or memories.

Self-Reported Accounts

Information provided by individuals about themselves, often used in research to gather data on behaviors, attitudes, and experiences.

Confirmation Bias

The propensity to accumulate, perceive, select, and keep in mind information that endorses an individual's longstanding beliefs or propositions.