Find the Interval of Convergence Of $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } ( x + 2 ) ^ { n } } { \sqrt { n } 3 ^ { n } }$

question 110

Multiple Choice

Find the interval of convergence of $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } ( x + 2 ) ^ { n } } { \sqrt { n } 3 ^ { n } }$ .

• A) \(( - \infty , \infty )\)
• B) \(( - 5,1 ]\)
• C) \([ - 5,1 )\)
• D) \([ - 5,1 ]\)
• E) \(( - 4,0 ]\)
• F) \([ - 4,0 )\)
• G) \([ - 4,0 ]\)
• H) \(( - 3 , - 1 )\)

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Definitions:

Albert Ellis

An influential American psychologist who developed Rational Emotive Behavior Therapy (REBT), emphasizing the role of beliefs in psychological health.

Magnitude of Problems

The extent or size of difficulties or issues, often indicating their significance or severity.

Defense Mechanisms

Psychological strategies brought into play by the unconscious mind to manipulate, deny, or distort reality in order to defend against feelings of anxiety and unacceptable impulses.

Unconscious Level

Mental processes that occur without conscious awareness or control.