Select the Right Expression for the Following Sum and Prove $n$

question 216

Multiple Choice

Select the right expression for the following sum and prove that your statement is true for all natural numbers $n$ .
$$P _ { \mathrm { n } } : 8 + 6 + 4 \ldots ( 10 - 2 n )$$

• A) \(\quad 11 n - 2 n ^ { 2 }\)
• B) \(\quad 9 n - n ^ { 2 }\)
• C) \(\quad 11 n - n ^ { 2 }\)
• D) \(\quad 9 n - 2 n ^ { 2 }\)
• E) none of the above

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Definitions:

Profit-Maximizing

This refers to the process businesses use to determine the output level at which profits are at their highest.

Marginal Revenue Curve

A graph that displays how additional revenue is affected by the sale of one more unit of a product or service.

Downsloping

describes a trend or curve that goes downward, often used in economics to describe demand curves where price decreases lead to an increase in quantity demanded.

Economic Profits

Profits exceeding the opportunity costs of a venture or investment, accounting for both explicit and implicit costs.