Use the Summation Properties to Evaluate the Series - $$\sum _ { i = 1 } ^ { 5 } \left( 3 + 2 i ^ { 3 } \right)$$

question 275

Multiple Choice

Use the summation properties to evaluate the series. The following rules may be needed: $$\sum _ { i = 1 } ^ { n } i = \frac { n ( n + 1 ) } { 2 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 3 } = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 }$$
- $$\sum _ { i = 1 } ^ { 5 } \left( 3 + 2 i ^ { 3 } \right)$$

• A) 685
• B) 465
• C) 1125
• D) 915

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Definitions:

Regression Analysis

A statistical method for estimating the relationships among variables, often used to predict the value of one variable based on others.

Independent Variables

Variables in an experimental setup that are changed or controlled to test their effects on dependent variables.

Observations

The individual data points or recorded measures of variables collected during a research study or experiment.

Estimated Regression Equation

A mathematical formula predicting the relationship between the dependent variable and one or more independent variables, derived from regression analysis.