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

question 44

Multiple Choice

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

• A) \([ - 1,1 ]\)
• B) \(( - 1,1 )\)
• C) \(( - 1,1 ]\)
• D) diverges everywhere
• E) \([ - 1,1 )\)

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Definitions:

Long Run

A period in economic analysis during which factors of production and costs are fully adjustable, allowing all inputs to production to be varied.

Marginal Revenue

This refers to the additional income earned by selling one more unit of a good or service.

Marginal Cost

The additional cost incurred to produce one more unit of a good or service, highlighting the cost variations when adjusting production levels.

Fixed Costs

Expenses that do not change in proportion to the activity of a business, such as rent, salaries, and loan payments.