1.((1-1/3)*1/2+(1/2-1/4)*1/3+1/4(1/3-1/5)...+(1/98-1/100)*1/99)/2=(1*1/2-1/3*1/2+1/2*1/3-1/4*1/3+1/4*1/3-1/4*1/5.1/98*1/99-1/100*1/99)/2=(1/2-1/100*1/99)/2=4949/19800