1x1\3+2x1\4+3x1\5+.+2006x1\2008的简便算法

1x1\3+2x1\4+3x1\5+.+2006x1\2008的简便算法
1x1\3+2x1\4+3x1\5+.+2006x1\2008的简便算法

1x1\3+2x1\4+3x1\5+.+2006x1\2008的简便算法
1x1\3=1/2*(1/1-1/3)
2x1\4=1/2*(1/2-1/4)
.
1x1\3+2x1\4+3x1\5+.+2006x1\2008
=1/2(1/1-1/3+1/2-1/4+1/3-1/5+.+1/2005-1/2007+1/2006-1/2008)
=1/2(1+1/2-1/2007-1/2008)
=6041069/8060112

1x1\3=1/2(1/1-1/3)
2x1\4=1/2(1/2-1/4)
.......
=1/3+2/4+3/5+……+2006/2008
=1/2(1+1/2-1/2007-1/2008)
=1/2{1+(1-1/2)+(1/2-1/3)+(1/3-1/4)……（1/2007-1/2008）}
=1/2(1+1-1/2008)
=1/2(2-1/2008)
=1-1/4016
=4015/4016