注意到,1/8=1/2(1/2-1/4),1/24=1/2(1/4-1/6),1/48=1/2(1/6-1/8)..而1/9800=1/2(1/98-1/100),
所以1/8+1/24+1/48+.+1/9800=1/2(1/2-1/4)+1/2(1/4-1/6)+1/2(1/6-1/8)+.+1/2(1/98-1/100)=1/2(1/2-1/4+1/4-1/6+1/6-1/8+..+1/98-1/100)=1/2(1/2-1/100)=49/200.