1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90怎么做?
题目
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90怎么做?
给我理由!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
答案
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1-1/2+1/2-1/3+1/3-1/4+……1/9-1/10 (除了1与1/10,两两抵消)
=1-1/10
=9/10
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