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

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/11 12:59:09

（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

（1-1/2-1/3-1/4..-1/2004)*(1+1/2+1/3+1/4+...+1/2005)-(1-1/2-1 1/1*2+1/2*3+1/3*4+.+1/2004*2005+1/2005*2006 计算:(1/2006-1)(1/2005-1)(1/2004)… (1/3-1)(1/2-1). 1/1*2+1/3*4+1/4*5+...+1/2004*2005+1/2005*2006, 1*2/1+1/2*3+1/3*4...2004*2005/1+2005*2006/1+2006*2007/1 1*2/1+2*3/1+3*4/1+.+2004*2005/1= 1/2*1+1/2*3+1/3*4+.+1/2004*2005=? (1-2²/1)×(1-3²/1)×...(1-2004²/1)×(1-2005² (-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+(-1/4*1/5)+""+(-1/2005*1/2006 “简便计算：|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2005-1/2004 1+1/2+1/3+1/4+……+1/2004+1/2005+1/2006+1/2007+1/2008+1/2009+1 化简(1/2+1/3+...1/2003)*(1+1/2+...1/2004)-(1+1/2+...1/2004)*(1