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1/6＝1/2×1/3＝1/2-1/3,1/12＝1/3×1/4＝1/3-1/4,请你根据这个规律计算1/6+1/12+.+1/1980
题目详情
1/6＝1/2×1/3＝1/2-1/3 ,1/12＝1/3×1/4＝1/3-1/4 ,请你根据这个规律计算1/6+1/12+.+1/1980
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答案和解析
1/6+1/12+.+1/1980
=1/2×1/3+1/3×1/4+.+1/44×1/45
=1/2-1/3+1/3-1/4.+1/44-1/45
=1/2-1/45
=43/90
=1/2×1/3+1/3×1/4+.+1/44×1/45
=1/2-1/3+1/3-1/4.+1/44-1/45
=1/2-1/45
=43/90
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