(1²+3²)/(2²-1)+(2²+4²)/(3²-1)+(3²+5²)/(4²-1)+……+（99²+100²）/(99²-1)=

(1²+3²)/(2²-1)+(2²+4²)/(3²-1)+(3²+5²)/(4²-1)+……+（99²+100²）/(99²-1)=
(1²+3²)/(2²-1)+(2²+4²)/(3²-1)+(3²+5²)/(4²-1)+……+（99²+100²）/(99²-1)=

(1²+3²)/(2²-1)+(2²+4²)/(3²-1)+(3²+5²)/(4²-1)+……+（99²+100²）/(99²-1)=
∵a/b+b/a=(a^2+b^2)/ab,
又∵c^2-1=(c+1)×(c-1)
∴原式 ＝1/3+3/1+2/4+4/2+3/5+5/3+.+98/100+100/98
＝(1/3+2/4+3/5+4/6+5/7+.+95/97+96/98+97/99+98/100)+
[3/1+4/2+(1+2/3)+(1+2/4)+(1+2/5)+.+(1+2/97)+(1+2/98)]
＝ [(1/3+2/4+3/5+4/6+5/7+.+95/97+96/98) +97/99+98/100]+
[3+2+96+(2/3+2/4+2/5+2/6+2/7+.+ 2/97 + 2/98)]
＝3+2+96+96+97/99+98/100
＝197+(97×100+98×99)/9900
＝198又9900分之9502
另及：原题最后一项分式表达式的分子项好像有暇疵,99^2应改为98^2才能和之前表达式一致.
最简分数我就不化简了,自己去作.