1*1/2+2*1/3+.+2009*1/2010这个式子结果是什么，最好能有解答过程

(1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/2009^2), 1/(1*1+1)+1/(2*2+2)+1/(3*3+3)+……1/(2009*2009+2009) 答案是 1/2009+2/2009+3/2009+.+2008/2009=? 1/1*2+1/2*3+...+1/2008*2009= ｜1/2-1｜+｜1/3-1/2｜+1/4-1/3｜+...｜1/2009-1/2008｜+｜1/2010-1/2009｜=? 1+2+3,+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| (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. 1/2009+2/2009+3/2009+.+2008/2009=?1/2+1/4+1/8+1/16+.+1/1024=? |1/2011-1/2010|+|1/2011-1/2009|+|1/2009-1/2008|+...+|1/3-1/2|+|1/2-1| 计算：|2/1-1|+|3/1-2/1|+|4/1-3/1|.+|2010/1-2009/1|? 简算1+1/(1+2)+1/(1+2+3)+.+1/(1+2+3+.+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+1/2+1/3+...1/2008)-(1+1/2+1/2009)(1/2+1/3+...+1/2008)答案等于多少? (1-1/2)(1/3-1)(1-1/4)(1/5-1)``````(1/2009)(11/2010) 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= 计算 (1/2+1/3+.+1/2010)(1+1/2+1/3+.+1/2009)-(1+1/2+1/3+.+1/2010)1/2+1/3+.+1/2009)是计算 (1/2+1/3+....+1/2010)×(1+1/2+1/3+....+1/2009)-(1+1/2+1/3+....+1/2010)×（1/2+1/3+....+1/2009)