5/6+11/12+19/20+29/30+41/42
简便计算5/6+11/12+19/20+29/30+55/56+71/72=5/6+11/12+19/20+29/30+41/42+55/56+71/72...
简便计算 5/6+11/12+19/20+29/30+55/56+71/72=
5/6+11/12+19/20+29/30+41/42+55/56+71/72 展开
5/6+11/12+19/20+29/30+41/42+55/56+71/72 展开
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中间少了个+41/42吧?
5/6+11/12+19/20+29/30+41/42+55/56+71/72
=(1-1/6)+(1-1/12)+(1-1/20)+(1-1/30)+(1-1/42)+(1-1/56)+(1-1/72)
=7-(1/6+1/12+1/20+1/30+1/56+1/72)
=7-(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)
=7-(1/2-1/9)
=7-7/18
=6又11/18
5/6+11/12+19/20+29/30+41/42+55/56+71/72
=(1-1/6)+(1-1/12)+(1-1/20)+(1-1/30)+(1-1/42)+(1-1/56)+(1-1/72)
=7-(1/6+1/12+1/20+1/30+1/56+1/72)
=7-(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)
=7-(1/2-1/9)
=7-7/18
=6又11/18
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