Use the Summation Properties to Evaluate the Series - $$\sum _ { i = 1 } ^ { 6 } \left( i ^ { 2 } + i - 4 \right)$$

question 175

Multiple Choice

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

• A) 417
• B) 108
• C) 88
• D) 437

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Definitions:

Income Ratio

A financial metric used to gauge a company's profitability by comparing its income to other relevant figures, such as sales or assets.

Business Operations

The day-to-day activities involved in running a business, which include producing goods, providing services, and selling to customers.

Quality

The standard of something as measured against other similar things, or the degree of excellence of something.

Income Ratio

A financial metric measuring the efficiency or profitability of an organization, often represented as a comparison between income and some other relevant factor like sales or assets.