Question

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132=

详解一下

Answer 1

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132
=1/(1×2﹚+1/(2×3)+1/(3×4)+....+1/(11×12)
=1-1/2+1/2-1/3+1/3-1/4+....+1/11-1/12
=1-1/12
=11/12
这是我在静心思考后得出的结论，
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Answer 2

原式=1-1/2+1/2-1/3+1/3-1/4-1/4-1/5+1/5-1/6+......+1/11-1/12
=1-1/12
=11/12

追问

麻烦，给详解一下

追答

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132
=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+...... +1/12*11
=1-1/2+1/2-1/3+1/3-1/4-1/4-1/5+1/5-1/6+......+1/11-1/12
=1-1/12
=11/12

Answer 3