= 1 + 1/3 + 1/2009 - 1/2 + 1/4 + ... + 1/2010
= 1 + 1/2 + 1/3 + 1/4 + ... + 1/2009 + 1/2010 - 2 . 1/2 + 1/4 + 1/6 +..+ 1/2010
= 1 + 1/2 + 1/3 + ...+ 1/2010 - 1 + 1/2 + 1/3 + 1/1005
= 1/1006 + 1/1007 + ...+ 1/2010
= 1 + 1/3 + 1/2009 - 1/2 + 1/4 + ... + 1/2010
= 1 + 1/2 + 1/3 + 1/4 + ... + 1/2009 + 1/2010 - 2 . 1/2 + 1/4 + 1/6 +..+ 1/2010
= 1 + 1/2 + 1/3 + ...+ 1/2010 - 1 + 1/2 + 1/3 + 1/1005
= 1/1006 + 1/1007 + ...+ 1/2010
1 - 1/2 + 1 /3 - 1/4 + 1/5...........+ 1/2009-1/2010 = 1/1006 + 1007 +....... 1/2010
1-1/2+1/3-1/4+1/5-1/6+...+1/2011-1/2012 / 1006-1006/1007-1007/1008-1008/1009-...-2010/2011-2011/2012
a) 2010/1+2009/2+2008/3+ ... +1/2010+2010 : 1+1/2+1/3+ ... +1/2010=
b) 1/2011+1/2010+1/2009+ ... +1/3+1/2 : 2010/1+2009/2+2008/3+ ... +1/2010=
a = 1/2 nhân 2 + 1/3 nhân 3 + 1/4 nhân 4 + .....+ 1/2009 nhân 2009 + 1/2010 nhân 2010
so sánh a với 1
TÍNH TỔNG : 1/1 : 2 + 1/2 : 3 + 1/3 : 4 + .........+ 1/2009:2010 + 1/2010 : 2011
(1/2+1/3-1/4+...+1/2009-1/2010):(1/2006+1/2007+...+1/2010)
2010+ 2009/2 +.......+ 2/2009 +1/2010 =
1/2+1/3 +1/4 + ......+1/2010 +1/2011
tinh tong :
1/1:2+1/2:3+1/3:4+...+1/2009:2010+1/2010:2011
"1/2+1/3-1/4+...+1/2009-1/2010": "1/2006+1/2007+...+1/2010"
1 / 1 + 2009 / 2010 + 2009 / 2011 + 1 / 1 + 2000 / 2009 + 2010 / 2011 + 1 / 1 + 2011 / 2009 + 2011 /2010