Use the Summation Properties to Evaluate the Series - $$\sum _ { i = 1 } ^ { 3 } \left( i ^ { 2 } + i - 7 \right)$$

question 132

Multiple Choice

Use the summation properties to evaluate the series. The following rules may be needed: $$\sum _ { i = 1 } ^ { n } i = \frac { n ( n + 1 ) } { 2 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 3 } = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 }$$
- $$\sum _ { i = 1 } ^ { 3 } \left( i ^ { 2 } + i - 7 \right)$$

• A) 29
• B) 15
• C) 13
• D) \(- 1\)

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Definitions:

Average Income

The mean income of a group, calculated by dividing the total income of the group by the number of individuals or entities in that group.

Total Revenue

The total income a business receives from selling its goods or services, calculated by multiplying the price per unit by the number of units sold.

Demand Curve

A graphical representation showing the relationship between the quantity of a good that consumers are willing and able to purchase and its price.

Equation

A mathematical statement that asserts the equality of two expressions, typically involving variables and constants.