计算:1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10.

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/16 19:43:51
计算:1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10.计算:1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7

计算:1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10.
计算:1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10.

计算:1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10.
1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10
=1-1/2+1/2-1/3+1/3-.-1/9+1/9-1/10
=1-1/10
=9/10

1/1x2=1-1/2
1/2x3=1/2-1/3
........
1/9x10=1/9-1/10
1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10
=1-1/2+1/2-1/3+1/3-....-1/9+1/9-1/10
=1-1/10
=9/10