Use the Ratio Test to Examine the Two Series Below $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { 2 ^ { 2 n + 1 } } { 5 ^ { n } }$

question 13

Multiple Choice

Use the Ratio Test to examine the two series below, stating: absolute convergence (A) , divergence (D) , or Ratio Test inconclusive (I) .
1) $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { 2 ^ { 2 n + 1 } } { 5 ^ { n } }$
2) $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { 5 ^ { n } } { 2 ^ { 2 n + 1 } }$

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

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Definitions:

Absorption Costing

An accounting method that includes all manufacturing costs - direct materials, direct labor, and both variable and fixed manufacturing overhead - in the cost of a product.

Cost Behaviour

Refers to how a cost changes as the related level of activity or volume changes.

Fixed Expenses

Costs that do not change in total despite changes in the volume of goods or services produced or sold, such as rent or salary expenses.

Volatility

This refers to the degree of variation of a trading price series over time, typically measured by the standard deviation of logarithmic returns.