HMMT 2003 K6

For $n$ an integer, evaluate

$\lim _{n \rightarrow \infty}\left(\frac{1}{\sqrt{n^{2}-0^{2}}}+\frac{1}{\sqrt{n^{2}-1^{2}}}+\cdots+\frac{1}{\sqrt{n^{2}-(n-1)^{2}}}\right)$

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{\pi}{2}

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