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 将以上三个等式两边分别相加得: 1 1×2 + 1 2×3 + 1 3×4 =1- 1 2 + 1 2 - 1 3 + 1 3 - 1 4 =1- 1 4 = 3 4 (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 2009×2010 =______; 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 2008×2010 =______.