Which of the Three Series Below Converges?
1) $\sum _ { n = 0 } ^ { \infty } \left( - \frac { 3 } { 4 } \right) ^ { n }$

question 309

Multiple Choice

Which of the three series below converges?
1) $\sum _ { n = 0 } ^ { \infty } \left( - \frac { 3 } { 4 } \right) ^ { n }$ 2) $\sum _ { n = 0 } ^ { \infty } \left( \frac { e } { \pi } \right) ^ { n }$ 3) $\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n }$

• A)None
• B)1
• C)2
• D)3
• E)1, 2
• F)1, 3
• G)2, 3
• H)1, 2, 3

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Definitions:

Marginal-Cost Curve

A graphical representation showing how the cost of producing one additional unit of a good varies as the quantity of production changes.

Additive Manufacturing

A method that involves building items by depositing material in successive layers, widely referred to as 3D printing.

Fixed Set-Up Costs

Initial costs that do not vary with the level of production or sales, such as equipment purchases or facility leases, needing to be paid before production starts.

Economies of Scale

The savings businesses gain from operating at a larger scale, where the expense for each unit produced diminishes as the scale enlarges.