Find the Radius of Convergence of the Series $\sum _ { n = 1 } ^ { \infty } \frac { n ^ { n } ( x + 1 ) ^ { n } } { 3 ^ { n } }$

question 118

Multiple Choice

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

• A)0
• B)2
• C)3
• D)4
• E) \(\frac { 1 } { 2 }\)
• F)1
• G)5
• H) \(\infty\)

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Definitions:

Rationalism

The view that knowledge is best acquired by reason and factual analysis rather than faith or emotion.

Positivism

The idea that phenomena are governed by, and can be explained by, rules based on objective observation and generalizations from those observations.

Explanation

An attempt to account for the relationships observed among phenomena. A basic goal of communications research is to explain how and why communication phenomena occur.

Two-tailed Hypothesis

A type of hypothesis that predicts either an increase or decrease in outcomes, requiring evidence for significant change in either direction.