计算:2^2/1*3+3^2/2*4+...+99^2/98*100.

每个分数的分子都比分母大1.比如：98*100=(99-1)(99+1)=99^2-1
所以原式＝(1+1/1*3)+(1+1/2*4)+.+(1+1/98*100)
=98+(1/1*3+1/2*4+1/3*5+...+1/98*100)
=98+(1/1*3+1/3*5+...+1/97*99)+(1/2*4+1/4*6+...+1/98*100)
=98+1/2*(1-1/3+1/3-1/5+...+1/97-1/99)+1/2*(1/2-1/4+1/4-1/6+...+1/98-1/100)
=98+1/2(1-1/99)+1/2*(1/2-1/100)
=98+1/2*98/99+1/2*49/100
=98+49/99+49/200
=98+49*299/19800