请教数学题(6+1/42+7+1/56+8+1/72.+20+1/420=?请把答案道理写清楚,

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请教数学题(6+1/42+7+1/56+8+1/72.+20+1/420=?请把答案道理写清楚,

请教数学题(6+1/42+7+1/56+8+1/72.+20+1/420=?请把答案道理写清楚,
请教数学题(6+1/42+7+1/56+8+1/72.+20+1/420=?
请把答案道理写清楚,

请教数学题(6+1/42+7+1/56+8+1/72.+20+1/420=?请把答案道理写清楚,
6+1/42+7+1/56+8+1/72.+20+1/420
=6+7+8+...+20+1/42+1/56+1/72+...+1/420
=[(6+20)*7+13]+(1/6*7)+(1/7*8)+(1/8*9)+...+(1/20*21)
=195+1/6-1/7+1/7-1/8+1/8-1/9+...+1/20-1/21
=195+1/6-1/21
=195+7/42-2/42
=195+5/42
=195又5/42

答案,195+5/42
裂分法,例如:1/42=1/6*7=1/6-1/7

原题=(6+7+....+20)+(1/6-1/7+1/7-1/8+....+1/20-1/21)