$$\lim_{x \to \infty}\:\: \frac{1+2+3+...x}{x^2} $$ How can I find the limit of above expression. Please tell me which identities and theorems to apply.
2026-05-14 11:33:24.1778758404
Help me to find the limit of the given function
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You can observe the sum of the first $n$ numbers corresponds to
$\sum_{k=1}^n k=\frac{n(n+1)}{2}$
This means
$\lim_{n\to \infty} \frac{n(n+1)}{2n^2}=\frac{1}{2}$