Which One of the Following Series Diverges?
A) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 1.0001 } }$

question 47

Multiple Choice

Which one of the following series diverges?

• A) \(\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 1.0001 } }\)
• B) \(\sum _ { n = 1 } ^ { \infty } \left( \frac { \pi } { 4 } \right) ^ { n }\)
• C) \(\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n + e ^ { n } }\)
• D) \(\sum _ { n = 1 } ^ { \infty } \frac { n + n ^ { 3 } } { n ^ { 4 } + 1 }\)
• E)None of these

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Definitions:

Total Revenue

The price of a good or service multiplied by the number of units sold.

Marginal Revenue Product

The additional revenue generated from employing one more unit of a resource, factor of production, or input.

Perfect Competition

An industry with so many firms that no one firm has any influence over price, and firms produce an identical product.

Imperfect Competition

All market structures except perfect competition; includes monopoly, oligopoly, and monopolistic competition.