Express the Sum Using Summation Notation $$( a + 1 ) + ( a + b ) + \left( a + b ^ { 2 } \right) + \ldots + \left( a + b ^ { n } \right)$$

question 94

Multiple Choice

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of
summation.
- $$( a + 1 ) + ( a + b ) + \left( a + b ^ { 2 } \right) + \ldots + \left( a + b ^ { n } \right)$$

• A) \(\sum _ { \mathrm { k } = 1 } ^ { \mathrm { n } } \left( \mathrm { a } + \mathrm { b } ^ { \mathrm { k } } \right)\)
• B) \(\sum _ { \mathrm { k } = 0 } ^ { \mathrm { n } } a \mathrm {~b} ^ { \mathrm { k } }\)
• C) \(\sum _ { k = 0 } ^ { n } \left( a + b ^ { k } \right)\)
• D) \(\sum _ { k = 0 } ^ { n - 1 } \left( a + b ^ { k } \right)\)

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Definitions:

Perfectly Elastic

Describes a market situation where the quantity demanded or supplied changes infinitely with even a slight change in price, indicating extreme sensitivity.

Price-taker Industry

A Price-taker Industry is one in which individual firms have no control over the price of their product and must accept the market price as determined by supply and demand.

Constant Cost Industry

An industry wherein the costs of production do not change as the overall level of output increases or decreases.

Entry Barriers

Obstacles that prevent new competitors from easily entering an industry or area of business, including high startup costs, licensing requirements, and access to technology.