简便运算：1/2+（-1/6）+(-1/12)+（-1/20)+(-1/30)+(-1/42)=?

来源：百度知道 编辑：UC知道 时间：2024/05/21 12:26:10
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1/2+ 1/6+ 1/12+ 1/20+1/30 +1/42
=1/2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7

1/2+（-1/6）+(-1/12)+（-1/20)+(-1/30)+(-1/42)
=1/2+[-1/(2*3)]+[-1/(3*4)]+[-1/(4*5)]+[-1/(5*6)]+[-1/(6*7)]
注:1/[N(N+1)]=1/N-1(N+1)
=1/2-1/2+1/3.........-1/6+1/7
=1/7

1/2+（-1/6）+(-1/12)+（-1/20)+(-1/30)+(-1/42)=1/2-1/(2*3)-1/(3*4)-1/(4*5)-1/(5*6)-1/(6*7)=1/2-(1/2-1/3)-(1/3-1/4)....(1/6-1/7)=1/2-1/2+1/3-1/3....+1/6-1/6+1/7=1/7

原式=1/2-1/6-1/12-1/20-2/30-1/42
=1/2-(1/2*1/3)-(1/3*1/4)-(1/4*1/5)-(1/5*1/6)-(1/6*1/7)
=1/2-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-(1/5-1/6)-(1/6-1/7)
=1/2-1/2+1/3-1/3+1/4-1/4+1/5-1/5+1/6-1/6+1/7
=1/7