化简1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)+...+1/(x+99)(x+102)
来源:学生作业帮 编辑:大师作文网作业帮 分类:数学作业 时间:2024/09/26 04:27:44
化简1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)+...+1/(x+99)(x+102)
1/x(x+3)=1/3(1/x-1/x+3)
1/(x+3)(x+6)=1/3(1/x+3-1/x+6)
.
1/(x+99)(x+102)=1/3(1/x+99-1/x+102)
1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)+...+1/(x+99)(x+102)=1/3(1/x-1/x+3)+1/3(1/x+3-1/x+6)
+.+1/3(1/x+99-1/x+102)=1/3(1/x-1/x+102)=34/x(x+102)
1/(x+3)(x+6)=1/3(1/x+3-1/x+6)
.
1/(x+99)(x+102)=1/3(1/x+99-1/x+102)
1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)+...+1/(x+99)(x+102)=1/3(1/x-1/x+3)+1/3(1/x+3-1/x+6)
+.+1/3(1/x+99-1/x+102)=1/3(1/x-1/x+102)=34/x(x+102)
|X-1|+|X-2|+|X-3|+|X-4|+|X-5|+|X-6|+|X-7|+|X-8|+|X-9|+|X-10|
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