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

question 297

Multiple Choice

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

• A) \(- 80\)
• B) \(- 50\)
• C) 40
• D) \(- 70\)

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Involves services and goods provided by the government or public entities to ensure welfare and infrastructure availability to the public.

Rent-seeking

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Short-sightedness Effect

The tendency of decision makers to prioritize immediate benefits at the expense of long-term gains.

Externalities

Costs or benefits that affect a party who did not choose to incur those costs or benefits, often leading to market failure if unaddressed by policy.