【教学过程】一、创设情境,引出课题情境一:问:1请同学们观察以上等式,可以猜想出什么结论?2对于以上问题,你能完成证明吗?注:1对于第一个问题,由于学生在学习求曲边梯形面积时已经用过,再结合归纳推理,学生很容易得出结论;1×2=1/3·1·2·3,1×2+2×3=1/3·2·3·4,1×2+2×3+3×4=1/3·3·4·5,1×2+2×3+3×4+4×5=13·4·5·6,1×2+2×3+3×4+……+n×(n+1)=1/3·n·(n+1)·(n+2) [Teaching process] First, create the situation, leads to the situation Scenario 1: Q: 1 students are invited to observe the above equation, you can guess what the conclusion? 2 for the above questions, you can complete the proof? Note: 1 for the first question , Because students have been learning to find the trapezoidal area of ​​the curved edge, and then combined with inductive reasoning, students can easily draw a conclusion; 1 × 2 = 1/3 · 1 · 2 · 3, 1 × 2 + 2 × 3 = 1 / 3 · 2.3 · 4 · 1 × 2 + 2 × 3 + 3 × 4 = 1/3 · 3.4 · 5 · 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 = 13 · 4 · 5 · 6,1 × 2 + 2 × 3 + 3 × 4 + ··· + n × (n + 1) = 1/3 · n · (n + 1) · (n + 2)