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请先阅读下列一组内容,然后解答问题: 先观察下列等式: 1 1×2 =1- 1 2 , 1 2×3 = 1 2 - 1 3 , 1 3×4 = 1 3 - 1 4 … 1 9×10 = 1 9 - 1 10 将以上等式两边分别相加得: 1 1×2 + 1 2×3 + 1 3×4 +…+ 1 9×10 = +( 1 2 - 1 3 )+( 1 3 - 1 4 )+…+( 1 9 - 1 10 ) = 1 2 - 1 3 + 1 3 - 1 4 +…+ 1 9 - 1 10 = 1- 1 10 = 9 10 然后用你发现的规律解答下列问题: (1)猜想并写出: 1 n(n-1) =______; (2)直接写出下列各式的计算结果: ① 1 1×2 + 1 2×3 + 1 3×4 +…+ 1 2010×2011 =______; ② 1 1×2 + 1 2×3 + 1 3×4 +…+ 1 n(n+1) =______; (3)探究并计算: 1 2×4 + 1 4×6 + 1 6×8 +…+ 1 2012×2014 .