1/2+5/6-7/12+9/20-11/30+13/42-1/7(裂项问题,
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1/2+5/6-7/12+9/20-11/30+13/42-1/7(裂项问题,
1/2+5/6-7/12+9/20-11/30+13/42-1/7(裂项问题,
1/2+5/6-7/12+9/20-11/30+13/42-1/7(裂项问题,
1/2+5/6-7/12+9/20-11/30+13/42-1/7
=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
=1-1/2+1/2+1/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7
=1
1/2+5/6-7/12+9/20-11/30+13/42-1/7
=1/2+(1/2+1/3)-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+(1/6+1/7)-1/7
=1/2+1/2
=1
原式=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
原式=1/2+(10-7)/12+(27-22)/60+(13-6)/42
=1/2+1/4+1/12+1/6
=(9+1+2)/12
=1
∵2n+1/n(n+1)=1/n+1/n+1
∴原式=1/2+(2+3/2*3)-(3+4/3*4)+(4+5/4*5).....+(6+7/6*7)-1/7
=1/2+1/2+1/3-[(1/3+1/4)+(1/4+1/5)]-.....+(1/6+1/7)-1/7
=1/2+1/2+1/3-1/3-1/4+1/4+1/5-.....+1/6+1/7-1/7
=1/2*2
=1
中间各项能够约掉,例如-1/4+1/4=0
望采纳谢谢