问两道数学题
1、 1/1*3+1/3*5+1/5*7+.....+1/2003*2005
2、 1/1*6+1/6*11+1/11*16+....+1/2001*2006
参考答案:1、 1/1*3+1/3*5+1/5*7+.....+1/2003*2005
=1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+......+1/2*(1/2003-1/2005)
=1/2*(1-1/3+1/3-1/5+1/5-1/7+......+1/2003-1/2005)
=1/2*(1-1/2005)
=1/2*2004/2005
=1002/2005
2、 1/1*6+1/6*11+1/11*16+....+1/2001*2006
=1/5*(1-1/6)+1/5*(1/6-1/11)+1/5*(1/11-1/16)+......+1/5*(1/2001-1/2006)
=1/5*(1-1/6+1/6-1/11+1/11-1/16+......+1/2001-1/2006)
=1/5*(1-1/2006)
=1/5*2005/2006
=401/2006