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i1/2一1i+i1/3一1/2i+丨1/4一1/3i十…+i1/2011一1/2010|+i12011一1/2012i
题目详情
i1/2一1i+i1/3一1/2i+丨1/4一1/3i十…+i1/2011一1/2010|+i1
2011一1/2012i
2011一1/2012i
▼优质解答
答案和解析
|1/2-1|+|1/3-1/2|+|1/4-1/3|+……+|1/2011-1/2010|+|1/2011-1/2012|
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2010-1/2011)+(1/2011-1/2012)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2010-1/2011+1/2011-1/2012
=1-1/2012
=2011/2012
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2010-1/2011)+(1/2011-1/2012)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2010-1/2011+1/2011-1/2012
=1-1/2012
=2011/2012
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