写出方法,过程
来源:百度知道 编辑:UC知道 时间:2024/07/02 06:20:56
4/3+16/15+36/35+64/63+100/99+144/143+196/195+256/255=
4/3+16/15+36/35+64/63+100/99+144/143+196/195+256/255
=[1+1/3]+[1+1/15]+[1+1/35]...+[1+1/255]
=1*8+1/1*3+1/3*5+1/5*7+....+1/15*17
=8+1/2[1-1/3]+1/2[1/3-1/5]+1/2[1/5-1/7]+...+1/2[1/15-1/17]
=8+1/2[1-1/3+1/3-1/5+...+1/15-1/17]
=8+1/2[1-1/17]
=8+1/2*16/17
=8又8/17
4/3+16/15+36/35+64/63+100/99+144/143+196/195+256/255
=8+(1/3+1/15+1/35+....+1/225)
=8+1/2(1-1/3+1/3-1/5+......+1/15-1/17)
=8+1/2(1-1/17)
=144/17