Express the Sum Using Summation Notation $\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 11 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 11 }$

question 67

Multiple Choice

Express the sum using summation notation.
- $\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 11 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 11 }$

• A)
• \(\sum _ { k = 1 } ^ { 11 } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { k }\)
• B)
• \(\sum _ { k = 1 } ^ { 12 } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { k }\)
• C)
• \(\sum_{k=1}^{11}\left(\frac{4}{5}\right)^{k}\)
• D)
• \(\sum_{k=1}^{n}(-1)^{(k+1)}\left(\frac{4}{5}\right)^{k}\)

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Definitions:

Short Run

A time period in which at least one factor of production is fixed and cannot be changed, contrasting with the long run where all factors are variable.

Perfectly Competitive Firm

A company that operates in a market where there are many buyers and sellers, where it sells a homogeneous product and where there is free entry and exit from the market.

Marginal Cost

The bump in overall costs arising from the production of an additional product or service unit.

Profit Increase

A rise in the difference between a business's revenues and its expenses, indicating improved financial performance.