(1/2+1/3+...+1/2009)(1+1/2+1/3+...+1/2008)-(1+1/2+...+1/2009)(1/2+1/3+...1/2008)

来源：学生作业帮助网编辑：作业帮时间：2024/05/13 07:36:08

(1/2+1/3+...+1/2009)(1+1/2+1/3+...+1/2008)-(1+1/2+...+1/2009)(1/2+1/3+...1/2008)
(1/2+1/3+...+1/2009)(1+1/2+1/3+...+1/2008)-(1+1/2+...+1/2009)(1/2+1/3+...1/2008)

(1/2+1/3+...+1/2009)(1+1/2+1/3+...+1/2008)-(1+1/2+...+1/2009)(1/2+1/3+...1/2008)
令a=1/2+1/3+...+1/2008
原式=(a+1/2009)(1+a)-(1+a+1/2009)a
=a(1+a)+1/2009(1+a)-a(1+a)-1/2009a
=1/2009(1+a)-1/2009a
=1/2009+1/2009a-1/2009a
=1/2009

令a=1/2+1/3+...+1/2008
原式=(a+1/2009)(1+a)-(1+a+1/2009)a
=a(1+a)+1/2009(1+a)-a(1+a)-1/2009a
=1/2009(1+a)-1/2009a
=1/2009+1/2009a-1/2009a
=1/2009

(1/2+1/3+...+1/2009)(1+1/2+1/3+...+1/2008)-(1+1/2+...+1/2009)(1/2+1/3+...1/2008)=
(1/2+1/3+...+1/2009)+(1/2+1/3+...+1/2009)(1/2+1/3+...+1/2008)-(1/2+1/3+...1/2008)-
(1/2+...+1/2009)(1/2+1/3+...1/2008)=1/2009

1/2009+2/2009+3/2009+.+2008/2009=? 1/2009+2/2009-3/2009-4/2009+5/2009+6/2009-7/2009-8/2009+9/2009+10/2009-...-1999/2009-2000/2009+2001/2009+2002/2009 1/(1*1+1)+1/(2*2+2)+1/(3*3+3)+……1/(2009*2009+2009) 答案是 1+2+3,+2009=? 1/2009+2/2009+3/2009+.+2008/2009=?1/2+1/4+1/8+1/16+.+1/1024=? ｜1/2-1｜+｜1/3-1/2｜+1/4-1/3｜+...｜1/2009-1/2008｜+｜1/2010-1/2009｜=? 1/1*2+1/2*3+...+1/2008*2009= 计算 |1/2011-1/2010|+|1/2010-1/2009|+|1/2009-1/2008|+...+|1/3-1/2|+|1/2-1|计算 |1/2011-1/2010|+|1/2010-1/2009|+|1/2009-1/2008|+...+|1/3-1/2|+|1/2-1| 1.2009/1+2009/2+2009/3+.2009/2008= 2.2/1+4/1+8/1+16/1+.+1024/1=2009/1+2009/2+2009/3+.2009/2008= 2/1+4/1+8/1+16/1+.+1024/1= (1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/2009^2), |1/2011-1/2010|+|1/2011-1/2009|+|1/2009-1/2008|+...+|1/3-1/2|+|1/2-1| (2011/1-1)(2010/1-1)(2009/1-1)…(3/1-1)(2/1-1) (1/2010-1)*(1/2009-1)*(1/2008-1)*...*(1/3-1)*(1/2-1)尽快. 计算：|2/1-1|+|3/1-2/1|+|4/1-3/1|.+|2010/1-2009/1|? (1/2+1/3+...+1/2009)(1+1/2+1/3+...+1/2008)-(1+1/2+...+1/2009)(1/2+1/3+...1/2008) (1/2+1/3+...1/2009)(1+1/2+1/3+...1/2008)-(1+1/2+1/2009)(1/2+1/3+...+1/2008)答案等于多少? 小学数学1/2009+2/2009+3/2009加到2007/2009+2008/2009怎样计算 1/2009+2/2009+3/2009+.2007/2009+2008/2009等于多少