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

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

#### Solution

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

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Q 15 | Page 77