Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • <img alt="\lim _{n \rightarrow \infty} \frac{3}{n}\left\{4+\left(2+\frac{1}{n}\right)^{2}+\left(2+\frac{2}{n}\right)^{2}+\cdots+\left(3-\frac{1}{n}\right)^{2}\right\}" src="https://entrancecorner.o

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

Option: 1

12


Option: 2

\frac{19}{3}


Option: 3

0


Option: 4

19


Answers (1)

best_answer

\lim _{x \rightarrow \infty} \frac{3}{n}\left\{\underset{\substack{4 \\ \uparrow \\(2+0/n)^{2}}}{ }(2+1 / n)^{2}+\left(2+\frac{2}{n}\right)^{2}+\ldots .+\left(3-\frac{1}{n}\right)^{2}\right\}
\Rightarrow \sum_{r=0}^{n-1} \frac{3}{n}\left(2+\frac{r}{n}\right)^{2}
\Rightarrow \int_{0}^{1} 3(2+x)^{2} d x
\Rightarrow\left[(2+x)^{3}\right]_{0}^{1}
\Rightarrow(2+1)^{3}-(2+0)^{3}
\Rightarrow 27-8=19

Posted by

shivangi.bhatnagar

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

Maharashtra to introduce policy for regulating coaching centres: Report
anam-khan

JEE Main 2026: BTech civil engineering cut-offs at NITs show steady demand after years of decline
anam-khan

JEE Main 2026 Registration LIVE: NTA to close applications on November 27, revises session 2 exam dates

Latest Question