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

---

Definitions:

Inequity

The perceived unfairness or imbalance in the distribution or treatment in social exchanges, leading to dissatisfaction and tension.

Outcomes

The results or effects that are a consequence of specific actions, processes, or behaviors.

Thistle Tube

A laboratory equipment used primarily in filtration and gas collection, featuring a funnel-like top and a long, narrow stem.

Fontanels

Soft, membranous gaps between the cranial bones of an infant's skull that facilitate birth and brain growth.