limn→∞[11⋅2+12⋅3+⋯+1n(n+1)]\lim\limits_{n\to\infty}\left[\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\cdots+\dfrac{1}{n(n + 1)}\right]n→∞lim[1⋅21+2⋅31+⋯+n(n+1)1]=（ ）.
limx→2x2−3x+2x2−4\lim\limits_{x\to 2}\dfrac{x^{2}-3x + 2}{x^{2}-4}x→2limx2−4x2−3x+2=（ ）.
求极限：limx→31+x−2sin(x−3)\lim\limits_{x\to 3}\dfrac{\sqrt{1 + x}-2}{\sin(x - 3)}x→3limsin(x−3)1+x−2.
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