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1÷(x+1)(x+3)+1÷(x+3)(x+5)+1÷(x+5)(x+7)+1÷(x+7)(x+9)+...+1÷(x

来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/05/26 05:36:58
1÷(x+1)(x+3)+1÷(x+3)(x+5)+1÷(x+5)(x+7)+1÷(x+7)(x+9)+...+1÷(x+2011)(x+2013)
1÷(x+1)(x+3)+1÷(x+3)(x+5)+1÷(x+5)(x+7)+1÷(x+7)(x+9)+...+1÷(x
1÷(x+1)(x+3)+1÷(x+3)(x+5)+1÷(x+5)(x+7)+1÷(x+7)(x+9)+...+1÷(x+2011)(x+2013)
=1/2*[1/(x+1)-1/(x+3)]+1/2*[1/(x+3)-1/(x+5)]+.+1/2*[1/(x+2011)-1/(x+2013)]
=1/2*[1/(x+1)-1/(x+2013)]
=1/2*[2012/(x+1)(x+2013)]
=1006/[(x+1)(x+2013)]