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

question 7

Short Answer

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

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Definitions:

Banishment

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Combination Act

Legislation passed in the United Kingdom during the early 19th century, specifically designed to restrict the activities of trade unions and prevent workers from organizing or striking.

Striking Workers

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Jailed Without Trial

The practice of detaining individuals without the opportunity to have a hearing or trial, often criticized for violating human rights and the principle of due process.