（1-1/2-1/3-1/4..-1/2004)(1+1/2+1/3+1/4+...+1/2005)-(1-1/2-1/3-1/4-...-1/2005)(1+1/2+1/3+1/4+...+1/2004)

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（1-1/2-1/3-1/4..-1/2004)*(1+1/2+1/3+1/4+...+1/2005)-(1-1/2-1/3-1/4-...-1/2005)*(1+1/2+1/3+1/4+...+1/

（1-1/2-1/3-1/4..-1/2004)*(1+1/2+1/3+1/4+...+1/2005)-(1-1/2-1/3-1/4-...-1/2005)*(1+1/2+1/3+1/4+...+1/2004)
（1-1/2-1/3-1/4..-1/2004)*(1+1/2+1/3+1/4+...+1/2005)-(1-1/2-1/3-1/4-...-1/2005)*(1+1/2+1/3+1/4+...+1/2004)

（1-1/2-1/3-1/4..-1/2004)*(1+1/2+1/3+1/4+...+1/2005)-(1-1/2-1/3-1/4-...-1/2005)*(1+1/2+1/3+1/4+...+1/2004)
原式=[1-(1/2+1/3+1/4.+1/2004)]*[1+(1/2+1/3+1/4+..+1/2005)]-[1-(1/2+1/3+1/4+..+1/2005)]*[
1+(1/2+1/3+1/4+...+1/2004)]把1/2+1/3+1/4.+1/2004看做a,1/2+1/3+1/4+..+1/2005看做b
则原式=(1-a)(1+b)-(1-b)(1+a)=2b-2a=1/2005*2=2/2005

设a=1-1/2-1/3-1/4-...-1/2004
b=1/2+1/3+1/4+...+1/2004
原式变为
a*（b+1/2005）-（a-1/2005）*b
= ab+a/2005-ab+b/2005
=（a+b）/2005
=（1-1/2-1/3-1/4-...-1/2004+1/2+1/3+1/4+...+1/2004）/2005
= 1/2005

设a=1-1/2-1/3-1/4-...-1/2004
b=1/2+1/3+1/4+...+1/2004+1/2005
axb-(a-1/2005)x(b-1/2005)=2/2005

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1+2+3+4. 1+2+3+4. 1+1+2+3+4.+99 1+2+3+4.=1/12? 1+2+3+4.+1000 1+2+3+4.+101 1+2+3+4..100000000 1+2+3+4.= 1/1+2+1/1+2+3+1/1+2+3+4+...+1/1+2+3+4...+992+1分之1加1+2+3/1这样 1/1*2+1/2*3+1/3*4.+1/2011*2012+1/2012*2013 1/1*2+1/2*3+1/3*4...+1/99*100+1/(2011*2012) （1-1/2-1/3-1/4..-1/2004)*(1+1/2+1/3+1/4+...+1/2005)-(1-1/2-1/3-1/4-...-1/2005)*(1+1/2+1/3+1/4+...+1/2004) （1-1/2+1/3-1/4.+1/1997-1/1998+1/1999)/[1/(1+1999)+1/(2+2000)+1/(3+2001).+1/(999+2997)+1/(1000+2998)] (1)计算1/1*2+1/2*3+1/3+4.+1/99*100 (2)1/1*3+1/3*5+1/5*7.+1/49*51 1/1*2+1/2*3+1/3*4...1/19*20=? 1/1乘2+1/2乘3+1/3乘4.+1/199乘200 1/1*2+1/2*3+1/3*4.+1/2003*2004 1/1×2+1/2×3+1/3×4...+1/2006×2007=?