7/12-9/20+11/30-13/42+…+23/132-25/156=

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7/12-9/20+11/30-13/42+…+23/132-25/156=
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7/12-9/20+11/30-13/42+…+23/132-25/156=
7/12-9/20+11/30-13/42+…+23/132-25/156=

7/12-9/20+11/30-13/42+…+23/132-25/156=
7/12-9/20+11/30-13/42+…+23/132-25/156
=1/3+1/4-1/4-/15+1/5+1/6-1/6-1/7+.+1/11+1/12-1/12-1/13=1/3-1/13=10/39

=(3+4)/3×4-(4+5)/4×5+(5+6)/5×6-(6+7)/6×7+……+(11+12)/11×12-(12+13)/12×13
=1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7+……+1/11+1/12-1/12-1/13
=1/3-1/13
=10/39


说明 (a+b)/ab=a/ab+b/ab=1/a+1/b

原式=1/3 1/4-1/4-1/5 1/5 1/6-1/6-1/7… 1/11 1/12-1/12-1/13=1/3-1/13=10/39