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

question 216

Multiple Choice

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

• A) \(\left( \frac { 2 } { 3 } , \frac { 4 } { 3 } \right]\)
• B) \(\left[ \frac { 2 } { 3 } , \frac { 4 } { 3 } \right)\)
• C) \(\left( \frac { 1 } { 2 } , \frac { 3 } { 2 } \right)\)
• D) \(\left[ \frac { 1 } { 2 } , \frac { 3 } { 2 } \right]\)
• E) \(( 0,2 ]\)
• F) \([ 0,2 )\)
• G) \(( - 1,3 )\)
• H) \([ - 2,4 ]\)

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Definitions:

Short-Run Aggregate Supply Curve

A graphical representation showing the relationship between the total production of goods and services and the price level for output in the short-run, acknowledging some input prices are fixed.

Nominal Wages

Wages that are paid to employees not adjusted for changes in price level, representing the amount of money received in the form of wages, before any deductions for taxes or other adjustments.

Aggregate Supply

The total supply of goods and services that firms in an economy plan on selling during a specific time period at various price levels.

Potential Output

The maximum amount of goods and services an economy can produce when it is most efficiently using all its resources.