巧思妙算1/1*2+1/2*3+1/3*4+………………+1/99*98+1又1/99*100巧思妙算

1/1*2+1/2*3+1/3*4+………………+1/99*98+1又1/99*100=(1-1/2)+(1/2-1/3)+(1/3-1/4)+………………+(1/98-1/99)+(1/99-1/100)中间正负抵消=1-1/100=99/100