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丨1-1/2丨+丨1/2-1/3/丨+|1/3-1/4|+……+|1/2013-1/2...

=1-1╱2014=2013╱2014

=1-1/2+1/2-1/3+……+1/9-1/10=1-1/10=9/10

中间各项相互抵消

原式=1-1/2015 =2014/2015

设(1-1/2-1/3-1/4-1/5)为a,(1/2+1/3+1/4+1/5)为b,代入得转化为a(b+1/6)-(a-1/6)b,得到ab+1/6a-ab+1/6b,化简为1/6(a+b),再重新代入,解得1/6(1-1/2-1/3-1/4-1/5+1/2+1/3+1/4+1/5)=1/6*1=1/6

-1/4+1/2ⅹ(2/3十丨2/3-2丨) =-1/4+1/2*(2/3+4/3) =-1/4+1/2*2 =-1/4+1 =3/4

1/(1x2)+1/(2x3)+1/(3x4)+...+1/(2012x2013) =(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2012-1/2013) =1 - 1/2013 =2012/2013

原式=(1/2-1/3) +(1/3-/14)+.....+(1/2012-1/2013)+(1/2013-1/2014) =1/2-1/2014 =1006/2014 =503/1007

通过提示可以知道,原式=(—1+1/2)+(-1/2+1/3)+(-1/3+1/4)+...(-1/2011+1/2012) 去掉括号然后得到-1+1/2-1/2+1/3-1/3...+1/2011-1/2011+1/2012=2013/2012 符号好难打啊!!

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