一道数学题 简算 1/1× 2× 3+1/2×3×4+1/3×4×5+······+1/9×10×11=?

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/19 19:46:16
一道数学题简算1/1×2×3+1/2×3×4+1/3×4×5+······+1/9×10×11=?一道数学题简算1/1×2×3+1/2×3×4+1/3×4×5+······+1/9×10×11=?一道

一道数学题 简算 1/1× 2× 3+1/2×3×4+1/3×4×5+······+1/9×10×11=?
一道数学题 简算 1/1× 2× 3+1/2×3×4+1/3×4×5+······+1/9×10×11=?

一道数学题 简算 1/1× 2× 3+1/2×3×4+1/3×4×5+······+1/9×10×11=?
1/1×2×3=(1/2)×(1/1×2-1/2×3)
1/2×3×4=(1/2)×(1/2×3-1/3×4)
……
1/9×10×11=(1/2)×(1/9×10-1/10×11)
所以原式=(1/2)×(1/1×2-1/2×3+1/2×3-1/3×4……+1/9×10-1/10×11)
=(1/2)×(1/1×2-1/10×11)
=(1/2)×(1/2-1/110)
=27/110

一个不好好学习的初中生??