1/1×2+1/2×3+1/3×4...+1/2006×2007=?
1*2/1+1/2*3+1/3*4...2004*2005/1+2005*2006/1+2006*2007/1
1/2009-1/2008|+|1/2008-1/2007|+|1/2007-1/2006|+.+|1/3-1/2|+|
|2009/1-2008/1|+|2008/1-2007/1|+|2007/1-2006/1|+.+|3/1-2/1|+
(1/2008-1)*(1/2007-1)*(1/2006-1)*...*(1/3-1)*(1/2-1)
(1+1/2+1/3+...+1/2006)*(1/2+1/3+1/4+...1/2007)-(1+1/2+1/3+..
①1/2+1/2*3+1/3*4+…+1/2006*2007=
1/2(x+1)+1/3(x+2)+1/4(x+3)+.+1/2007(x+2006)=2006
1+(-2)+(-3)+4...2005+(-2006)+(-2007)+2008+2009=...
2009-2008+2007-2006+~+3-2+1
2008+2007+2006…+3+2+1
2*1 1/2*1 1/3*1 1/4*1 1/5*.1 1/2006*1 1/2007
1/1*2+1/2*3+1/3*4+1/4*5+.+1/2006*2007