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

Short Answer

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