一道数学题 计算1-3/2+5/6-7/12+…-19/90+21/110 =
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1-3/2+5/6-7/12+…-19/90+21/110
= 1-(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+1/8)+(1/8+1/9)-(1/9+1/10)+(1/10+1/11)
=1-1-1/2+1/2+1/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7-1/8+1/8+1/9-1/9-1/10+1/10+1/11
=0+1/11=1/11
= 1-(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+1/8)+(1/8+1/9)-(1/9+1/10)+(1/10+1/11)
=1-1-1/2+1/2+1/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7-1/8+1/8+1/9-1/9-1/10+1/10+1/11
=0+1/11=1/11
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