Examine the Two Series Below for Absolute Convergence (A), Convergence $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { n + 1 } { \ln ( n + 1 ) }$

question 12

Multiple Choice

Examine the two series below for absolute convergence (A) , convergence that is not absolute (C) , or divergence (D) .
1) $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { n + 1 } { \ln ( n + 1 ) }$
2) $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { \ln ( n + 1 ) } { n + 1 }$

• A)1A, 2A
• B)1A, 2C
• C)1A, 2D
• D)1C, 2A
• E)1C, 2C
• F)1C, 2D
• G)1D, 2A
• H)1D, 2C

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Definitions:

Crossover Design

A research method where participants receive more than one treatment in a specific order, allowing comparison of different interventions within the same group.

Dependent Variable

The outcome variable being measured in an experiment or study, which is hypothesized to depend on or be affected by the independent variable(s).

Treatment Effectiveness

The degree to which a treatment achieves its intended outcome(s) in a real-world (clinical or practical) setting.

Between-Groups Designs

Experimental designs where different groups of participants are exposed to various conditions or treatments, allowing for comparisons between group outcomes.