若|a-1||+|ab-2|=0求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2005)(b+2005)还有就是|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/10-1/9|计算

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/02 22:19:43
若|a-1||+|ab-2|=0求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2005)(b+2005)还有就是|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/10-1/9|计算

若|a-1||+|ab-2|=0求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2005)(b+2005)还有就是|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/10-1/9|计算
若|a-1||+|ab-2|=0求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2005)(b+2005)
还有就是|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/10-1/9|计算

若|a-1||+|ab-2|=0求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2005)(b+2005)还有就是|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/10-1/9|计算
a=1,b=2
因为1/(1*2)=1/1-1/2 1/(2*3)=1/2-1/3
所以1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2005)(b+2005)
=1/(1*2)+1/(2*3)+1/(3*4)+...+1/(2006*2007)=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2006-1/2007)=1-1/2007=2006/2007
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/10-1/9|
=(1/2-1/3)+(1/3-1/4)+...+(1/8-1/9)+(1/9-1/10)
=1/2-1/10
=2/5