数学题1/1*3+1/3*5+1/5*7+．．．．1/97*99+1/99*101＝?

由于1/(2n-1)(2n+1)=[1/(2n-1)-1/(2n+1)]/2
所以1/3+1/3*5+1/5*7.1/99*101
=[(1-1/3)+(1/3-1/5)+...+(1/99-1/101)]/2
=(1-1/101)/2
=50/101