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

question 263

Multiple Choice

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

• A) 462
• B) 112
• C) 441
• D) 1764

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Definitions:

Sample Space

The set of all possible outcomes of a probability experiment.

Assign Probabilities

The process of allocating a likelihood or chance of occurrence to specific outcomes in a random event.

Sample Space

The collection of every potential result that can emerge from a statistical experiment.

Mutually Exclusive

A statistical term describing events that cannot occur at the same time.