Mathematics Question on Limits

Question

$\displaystyle\lim _{n \rightarrow \infty} \frac{3}{n}\left\\{4+\left(2+\frac{1}{n}\right)^2+\left(2+\frac{2}{n}\right)^2+\ldots+\left(3-\frac{1}{n}\right)^2\right\\}$ is equal to

Answer 1

Solution

The correct answer is (D) : 19
n→∞limn3r=0∑n−1(2+nr)2
=30∫1(2+x)2dx=27−8=19