$$\lim_{x \to \infty}\:\: \frac{1+2+3+...x}{x^2} $$ How can I find the limit of above expression. Please tell me which identities and theorems to apply.
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Is $x$ an integer number? – Federico Fallucca Oct 10 '20 at 07:02
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Yes it is a integral number – gauss19 Oct 10 '20 at 07:02
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related: https://math.stackexchange.com/questions/1667258/how-is-faulhabers-formula-derived – Anindya Prithvi Oct 10 '20 at 07:04
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Nope it's another question – gauss19 Oct 10 '20 at 07:05
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@gauss19, it looks exact same question to me. – cosmo5 Oct 10 '20 at 07:12
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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
$\lim_{n\to \infty} \frac{n(n+1)}{2n^2}=\frac{1}{2}$
Federico Fallucca
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