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

question 541

Multiple Choice

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

• A) 146
• B) 149
• C) 154
• D) 126

Understand the ideological and territorial expansion during the late 18th century in America.

Describe the American national identity and consciousness emerging post-Revolution.

Analyze the complexities of settlers moving west and their interactions with Native Americans.

Compare and contrast the Articles of Confederation with the Constitution, especially regarding sovereignty and economic policies.

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Definitions:

Frictional Energy

The energy that is generated by the friction between two surfaces moving against each other, often converted into heat.

Rotor Surface

The outer surface of a rotor, in systems like disc brakes, where frictional force is applied to slow down or stop the vehicle.

Cast Iron

A group of iron-carbon alloys with a relatively high carbon content, noted for their strength, wear resistance, and ability to withstand high temperatures.

Brake Rotors

The disc, most commonly made of cast iron, against which the caliper clamps the brake pads to slow the vehicle.