1×3分之1+3×5分之1+5×7分之1+……+97×99分之1

1/(1*3)+1/(3*5)+1/(5*7)+...+1/(97*99)
=[(1/1-1/3)+(1/3-1/5)+(1/5-1/7)+...+(1/97-1/99)]*1/2
=(1-1/99)/2
=98/99*1/2
=49/99