1道初中数学题目1/8+1/24+1/48+.+1/9800
问题描述：
1道初中数学题目
1/8+1/24+1/48+.+1/9800
答
1/8+1/24+1/48+1/80+......+1/9800
=(2/8+2/24+2/48+2/80+......+2/9800)/2
=[(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+......+(1/98-1/100)]/2
=(1/2-1/100)/2
=49/200
说实话这道题是别人解的，我是借鉴的
答
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.