Evaluate the Limit After First Finding the Sum (As a Function

question 135

Short Answer

Evaluate the limit after first finding the sum (as a function of $n$ ) using the summation formulas. $\lim _ { n \rightarrow \infty } \sum _ { k = 1 } ^ { n } \left( 4 + \frac { 2 k } { n } \right) ^ { 2 } \left( \frac { 1 } { n } \right)$

---

Definitions:

Deficit Principle

A concept in motivational theory suggesting that a satisfied need is not a motivator of behavior; individuals are motivated to fulfill unmet needs.

Motivator of Behaviour

Any stimulus that drives an individual to engage in a particular behavior, often aimed at achieving a specific outcome or reward.

Progression Principle

In fitness and training, the idea that the intensity and duration of exercise should increase gradually over time for optimal improvement.