1道初中数学题目1/8+1/24+1/48+.+1/9800
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1道初中数学题目
1/8+1/24+1/48+.+1/9800
1/8+1/24+1/48+.+1/9800
![1道初中数学题目1/8+1/24+1/48+.+1/9800](/uploads/image/z/1925454-30-4.jpg?t=1%E9%81%93%E5%88%9D%E4%B8%AD%E6%95%B0%E5%AD%A6%E9%A2%98%E7%9B%AE1%2F8%2B1%2F24%2B1%2F48%2B.%2B1%2F9800)
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.
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.