![](https://cos-cdn.shuashuati.com/pipixue-wap/2020-1230-1107-53/ti_inject-812ce.png)
观察算式: 1 1×2 =1- 1 2 = 1 2 , 1 1×2 + 1 2×3 =1- 1 2 + 1 2 - 1 3 = 2 3 1 1×2 + 1 2×3 + 1 3×4 =1- 1 2 + 1 2 - 1 3 + 1 3 - 1 4 = 3 4 按规律填空 1 1×2 + 1 2×3 + 1 3×4 + 1 4×5 =______ 1 1×2 + 1 2×3 + 1 3×4 + 1 4×5 +…+ 1 99×100 =______; 如果n为正整数,那么 1 1×2 + 1 2×3 + 1 3×4 + 1 4×5 +…+ 1 n×(n+1) =______. 由此拓展写出具体过程, 1 1×3 + 1 3×5 + 1 5×7 +…+ 1 99×101 =______.