分数数列求和
12分之1+20分之1+30分之1+42分之1+56分之1+72分之1+90分之1+110分之1+132分之1...
12分之1+20分之1+30分之1+42分之1+56分之1+72分之1+90分之1+110分之1+132分之1
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1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132
=1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+1/(7×8)+1/(8×9)+1/(9×10)+1/(10×11)+1/(11×12)
=(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)+(1/10-1/11)+(1/11-1/12)
=1/3-1/12
=1/4
=1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+1/(7×8)+1/(8×9)+1/(9×10)+1/(10×11)+1/(11×12)
=(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)+(1/10-1/11)+(1/11-1/12)
=1/3-1/12
=1/4
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