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[tex]\lim\limits_{n\to \infty}\left(\dfrac{n-1}{n+1}\right)^n;\ \lim\limits_{n\to \infty} (\sqrt{n^2+2n}-n)^n; \ \ \lim\limits_{n\to \infty}(n+1)(\ln(n^2+n+1)-\ln(n^2-n+1))[/tex]
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