1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90要有解题过程

1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90要有解题过程
1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90要有解题过程

1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90要有解题过程
1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+1/(7×8)+1/(8×9)+1/(9×10)
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1/2-1/10
=5/10-1/10
=4/10
=2/5
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1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1/(2x3)+1/(3x4)+...+1/(9x10)
= (1/2-1/3)+(1/3-1/4)+..+(1/9-1/10)
=1/2 -1/10
=2/5

=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1/2-1/10
=2/5