1/42+1/56+1/72+1/90+1/110
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![1/42+1/56+1/72+1/90+1/110](/uploads/image/z/36915-51-5.jpg?t=1%2F42%2B1%2F56%2B1%2F72%2B1%2F90%2B1%2F110)
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1/42+1/56+1/72+1/90+1/110
1/42+1/56+1/72+1/90+1/110
1/42+1/56+1/72+1/90+1/110
1/42+1/56+1/72+1/90+1/110
=1/(6×7)+1/(7×8)+1/(8×9)+1/(9×10)+1/(10×11)
=1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11
=1/6-1/11
=5/66
(请注意:1/42=1/(6×7)=1/6-1/7,后面方法相同.这是解题的关键)
=1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11=1/6-1/11=1/66