UC知道2/(2*4)+2/(4*6)+2/(6*8)+........2/(96*98)+2/(98*100)
来源：百度知道 编辑：UC知道 时间：2024/05/09 00:26:54
简便方法 快 今天用
2/(2*4)+2/(4*6)+2/(6*8)+........2/(96*98)+2/(98*100)
=1/2-1/4+1/4-1/6+..............+1/98-1/100
=1/2-1/100
=49/100
1/2-1/4+1/4-1/8+1/8 .....
=（1/2-1/4）+（1/4-1/6）+（1/6-1/8）…………+(1/98-1/100)
=1/2-1/100
=49/100
1/(2*4)=(1/2)*(1/2-1/4)
1/(4*6)=(1/2)*(1/4-1/6)
........
1/(98*100)=(1/2)*(1/98-1/100)
所以
2/(2*4)+2/(4*6)+2/(6*8)+........2/(96*98)+2/(98*100)
=(1/2-1/4)+(1/4-1/6)+........+（1/98-1/100）
=1/2-1/100
=98/200
=49/100
(或者0.49)
将分子分母上下同除以4，变为0.5[1/(1*2)+1/(2*3)+......+1/(48*49)+1/(49*50)]
=0.5(1-1/2+1/2-1/3+1/3-.......+1/48-1/49+1/49-1/50)
=0.5(1-1/50)
=0.49
2/(2*4)+2/(4*6)+2/(6*8)+........2/(96*98)+2/(98*100)
=1/2-1/4+1/4-1/6+...+1/98-1/100
=1/2-1/100
=49/100