1/2x5+1/5x8+1/8x11+…………+1/2003x2006+1/2006x2009 = 这是我儿子的小学作业,我想不出简便算法……

1/2x5+1/5x8+1/8x11+…………+1/2003x2006+1/2006x2009=1/3x(3/2x5+3/5x8+.+3/2006x2009)=1/3x(1/2-1/5+1/5-1/8+...+1/2006-1/2009)=1/3x(1/2-1/2009)=1/3x2007/2009=669/2009