Use the Summation Properties to Evaluate the Series - $$\sum _ { i = 1 } ^ { 4 } \left( 3 i ^ { 2 } + i \right)$$

question 133

Multiple Choice

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

• A) 80
• B) 120
• C) 100
• D) 40

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Definitions:

Dependent Means

Refers to the average outcomes within groups that are related or paired, often used in the analysis of experiments or studies.

Individuals

Refers to distinct objects or entities being studied or observed in research or statistical analysis, often representing people, animals, or units in an experiment or survey.

Null Hypothesis

The presumption in statistical testing that there is no significant effect or difference, serving as the default position until evidence suggests otherwise.

Dependent Means

A statistical term often used in the context of comparing two sets of related or matched data to determine if there's a significant difference between them.