1/2+5/6+11/12+19/20+29/30+41/42

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1/2+5/6+11/12+19/20+29/30+41/42
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1/2+5/6+11/12+19/20+29/30+41/42
1/2+5/6+11/12+19/20+29/30+41/42

1/2+5/6+11/12+19/20+29/30+41/42
36/7
裂项相消
=6-(1/2+1/6+1/12+1/20+1/30+1/42)
=6-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7)
=6-6/7
=36/7

36/7
裂项相消
=6-(1/2+1/6+1/12+1/20+1/30+1/42)
=6-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7)
=6-6/7
=36/7

原式=(1-1/2)+(1-1/6)+(1-1/12)+(1-1/20)+(1-1/30)+(1-1/42)
=6-(1/2+1/6+1/12+1/20+1/30+1/42)=6-43/42等于4又42分之41

1/2+5/6+11/12+19/20+29/30+41/42
=8/6+11/12+19/20+29/30+41/42
=27/12+19/20+29/30+41/42
=192/60+29/30+41/42
=250/60+41/42
=432/84
=36/7

式子变为1/2+1-1/6+1-1/12+1-1/20+1-1/30+1-1/40再变为 1/2+1-(1/2-1/3)+1-(1/3-1/4)..以次类推把后面的多少分之一这样的形式 要保证减下来的还是原叔 然后把括号去掉 相抵消可得结果5又1/7