简便计算 1/6+1/12+1/20+1/30+……1/2008*2009如上

简便计算 1/6+1/12+1/20+1/30+……1/2008*2009如上
简便计算 1/6+1/12+1/20+1/30+……1/2008*2009
如上

简便计算 1/6+1/12+1/20+1/30+……1/2008*2009如上
1/6+1/12+1/20+1/30+……1/2008*2009
=1/(2*3)+1/(3*4)+1/(4*5)+……+1/(2008*2009)
=(3-2)/(2*3)+(4-3)/(3*4)+(5-4)/(4*5)+……+(2009-2008)/(2008*2009)
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/2008-1/2009
=1/2-1/2009
=2007/4018

1/6+1/12+1/20+1/30+……1/2008*2009
=1/2-1/3+1/3-1/4+1/4-1/5+-----+1/2008-1/2009
=1/2-1/2009
=2007/4018

解 1/6+1/12+1/20+1/30+……1/2008*2009=
1/2-1/3+1/3-1/4+1/4-1/5+。。。。。+1/2008-1/2009=
1/2-1/2009=2007/4018