1. Tardigrade
  2. Question
  3. Mathematics
  4. displaystyle lim n arrow ∞ (3/n) 4+(2+(1/n))2+(2+(2/n))2+ ldots+(3-(1/n))2 is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

JEE MainJEE Main 2023Limits and Derivatives

Solution:

$ \displaystyle\lim _{n \rightarrow \infty} \frac{3}{n} \displaystyle\sum_{r=0}^{n-1}\left(2+\frac{r}{n}\right)^2 $
$ =3 \int\limits_0^1(2+x)^2 d x=27-8=19$