1/2+1/6+1/12+1/20+.+1/2009×2010结果为多少

1/2+1/6+1/12+1/20+.+1/2009×2010结果为多少
1/2+1/6+1/12+1/20+.+1/2009×2010结果为多少

1/2+1/6+1/12+1/20+.+1/2009×2010结果为多少
1/2+1/6+1/12+1/20+.+1/2009×2010
=1-1/2+1/2-1/3+1/3-1/4+...+1/2009-1/2010
=1-1/2010
=2009/2010

1/2=1-1/2 1/6=1/2-1/3 1/12=1/3-1/4依次分解开…你会看到中间会约掉的…最终=1-1/2010哦，结果你算吧