文档介绍:学生姓名: 年级 小六 讲课时间 老师姓名 课时
课题
复****简便计算
教学目标
掌握简便运算方法
重 点
掌握简便运算方法
难 点
掌握简便运算方法
×+×+×
1/(1×2×3×4)+1/(2×3×4×5)+1/(3×4×5×6)+...+1/(7×8×9×10)
=(1/3)×[1/(1×2×3)-1/(2×3×4)]+(1/3)×[1/(2×3×4)-1/(3×4×5)]+(1/3)×[1/(3×4×5)-1/(4×5×6)]+...+(1/3)×[1/(7×8×9)-1/(8×9×10)]
=(1/3)×[1/(1×2×3)-1/(2×3×4)+1/(2×3×4)-1/(3×4×5)+1/(3×4×5)-1/(4×5×6)+...+1/(7×8×9)-1/(8×9×10)]
=(1/3)×[1/(1×2×3)-1/(8×9×10)]
=(1/3)×[(1/6)-(1/720)]
=(1/3)×(119/720)
=119/2160
仅供参考:
(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/+1/5+1/6)-(1+1/2+1/3+1/4+1/5+1/6)*(1/2+1/3+1/4+1/5)
设1+1/2+1/3+1/4+1/5=a 1/2+1/3+1/4+1/5=b
(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4+1/5+1/6)-(1+1/2+1/3+1/4+1/5+1/6)*(1/2+1/3+1/4+1/5)=a*(b+1/6)-(a+1/6)*b=1/6(a-b)=1/6
4/3-7