作业帮求1/2+1/6+1/12+1/20+……+1/90=?这道题的解
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求1/2+1/6+1/12+1/20+……+1/90=?这道题的解
求1/2+1/6+1/12+1/20+……+1/90=?这道题的解
求1/2+1/6+1/12+1/20+……+1/90=?这道题的解
1/2+1/6+1/12+1/20+……+1/90
=1/2 + 1/2*1/3 + 1/3*1/4 + 1/4*1/5 + .+ 1/9*1/10
=1/2 + 1/2 - 1/3 + 1/3 - 1/4 +1/4-1/5 + ...+ 1/9 - 1/10
= 1-1/10
=0.9
1/2+1/6+1/12+1/20+……+1/90
=1-1/2+1/2-1/3+1/3-1/4+……+1/9-1/10
=1-1/10
=9/10
裂项相消
1/2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
依此类推，中间的都抵消了
1/2+1/6+1/12+1/20+……+1/90
=1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/9-1/10
=1-1/10
=9/10