1/2+5/6+11/12+19/20+29/30+41/42+55/56+71/72+89/90+109/110=？
2个回答
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1/2+5/6+11/12+19/20+29/30+41/42+55/56+71/72+89/90+109/110
=（1-1/2)+(1-1/6)+(1-1/12)+(1-1/20)+(1-1/30)+(1-1/42)+(1-1/56)+(1-1/72)+(1-1/90)+(1-1/110)
=1+1+1+1+1+1+1+1+1+1-1/2-1/6-1/12-1/20-1/30-1/42-1/56-1/72-1/90-1/110
=10-(1-1/2)-(1/2-1/3)-(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)
=10-1+1/2-1/2+1/3-1/3+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
=10-1+1/11
=9+1/11
即九又十一分之一
=（1-1/2)+(1-1/6)+(1-1/12)+(1-1/20)+(1-1/30)+(1-1/42)+(1-1/56)+(1-1/72)+(1-1/90)+(1-1/110)
=1+1+1+1+1+1+1+1+1+1-1/2-1/6-1/12-1/20-1/30-1/42-1/56-1/72-1/90-1/110
=10-(1-1/2)-(1/2-1/3)-(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)
=10-1+1/2-1/2+1/3-1/3+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
=10-1+1/11
=9+1/11
即九又十一分之一
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1/2+5/6+11/12+19/20+29/30+41/42+55/56+71/72+89/90+109/110
=1-1/2+1-1/6+1-1/12+1-1/20+1-1/30+1-1/42+1-1/56+1-1/72+1-1/90+1-1/110
=10-(1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110)
=10-(1-1/2+1/2-1/3+1/3-1/4+...+1/10-1/11)
=10-(1-1/11)
=9又1/11
=1-1/2+1-1/6+1-1/12+1-1/20+1-1/30+1-1/42+1-1/56+1-1/72+1-1/90+1-1/110
=10-(1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110)
=10-(1-1/2+1/2-1/3+1/3-1/4+...+1/10-1/11)
=10-(1-1/11)
=9又1/11
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