S=2/(1×3)+2^2/(3×5)+2^3/(5×7)+…+2^49/(97×99)=(1-1/3)+2(1/3-1/5)+2^2(1/5-1/7)+...+2^48(1/97-1/99)=1+(2*1/液戚3-1/3)+(2^2*1/孙樱5-2*1/5)+(2^3*1/7-2^2*1/7)+...+(2^48*1/闹凯陵97-2^47*1/97)-2^48*1/99=1+1/3+2/5+2^2/7+2^3/9+...+2^47/97-2^48/99所以S-T=1-2^49/99