Question

\(\lim_{n\to\infty} \frac{1+2+3+\dots+n}{n^2}\) is

• A. 1
• B. \(\frac{1}{2}\)
• C. 0
• D. 2

Hint:

For limits at infinity of rational functions where the degree of the numerator equals the degree of the denominator:
The limit is simply the ratio of the coefficients of the highest power terms.
Here, the highest power is \( n^2 \), and the ratio of their coefficients is \( 1 / 2 \).

Answer 1

The Correct Option is B