Advertisement Remove all ads

Write the Value of Lim N → ∞ 1 + 2 + 3 + . . . + N N 2 . - Mathematics

Write the value of \[\lim_{n \to \infty} \frac{1 + 2 + 3 + . . . + n}{n^2} .\]

Advertisement Remove all ads

Solution

\[\lim_{n \to \infty} \left( \frac{1 + 2 + 3 . . . n}{n^2} \right)\]
\[ = \lim_{n \to \infty} \left( \frac{n\left( n + 1 \right)}{2 n^2} \right)\]
\[ = \lim_{n \to \infty} \left( \frac{\left( n + 1 \right)}{2n} \right)\]
\[ = \frac{1}{2} \lim_{n \to \infty} \left( 1 + \frac{1}{n} \right)\]
\[ = \frac{1}{2}\]

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Q 15 | Page 77
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×