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1/2+5/6+11/12+19/20+29/30=简便计算
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1/2+5/6+11/12+19/20+29/30=
简便计算
简便计算
▼优质解答
答案和解析
1/2+5/6+11/12+19/20+29/30
=(1-1/2)+(1-1/6)+(1-1/12)+(1-1/20)+(1-1/30)
=[1-(1-1/2)]+[1-(1/2-1/3)]+[1-(1/3-1/4)]+[1-(1/4-1/5)]+[1-(1/5-1/6)]
=1-1+1/2+1-1/2+1/3+1-1/3+1/4+1-1/4+1/5+1-1/5+1/6
=4+1/6
=4又1/6
=(1-1/2)+(1-1/6)+(1-1/12)+(1-1/20)+(1-1/30)
=[1-(1-1/2)]+[1-(1/2-1/3)]+[1-(1/3-1/4)]+[1-(1/4-1/5)]+[1-(1/5-1/6)]
=1-1+1/2+1-1/2+1/3+1-1/3+1/4+1-1/4+1/5+1-1/5+1/6
=4+1/6
=4又1/6
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