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

question 25

Multiple Choice

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

• A) 110
• B) 400
• C) 100
• D) 40

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Definitions:

Deadweight Loss

The loss of economic efficiency that occurs when the equitable balance of supply and demand is not achieved due to market distortion.

Tax Increases

Governmental action to raise the amount of money collected from taxes, often affecting income, sales, or property taxes.

Deadweight Loss

An inefficiency in the market where the total surplus of producer and consumer is not maximized due to factors like taxes or subsidies.

Elastic Demand

A situation where the quantity demanded of a good or service significantly changes in response to a change in price.