观察下列等式,1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4
问题描述:
观察下列等式,1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4
答
(1)1/n(n+1)=1/n-1/(n+1)
(2)1/1x2+1/2x3+1/3x4+……+1/2009/2010
=1-1/2+1/2-1/3+1/3-1/4+……+1/2009-1/2010
=1-1/2010
=2009/2010
1/1x2+1/2x3+1/3x4+……+1/n(n+1)
=1-1/2+1/2-1/3+1/3-1/4+……+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
(3)1/2x4+1/4x6+1/6x8+……+1/2008x2010
=1/2x(1/2-1/4+1/4-1/6+1/6-1/8+……+1/2008-1/2010)
=1/2x(1/2-1/2010)
=1/2x502/1005
=251/1005