4/3+16/15+36/35+64/63+100/99+144/143+196/195+256/255怎么计算怎么计算4/3+16/15+36/35+64/63+100/99+144/143+196/195+256/255=?注意,分子总是比分母大“1”.有什么简便方法?

原式=（1+1/3）+(1+1/15)+(1+1/63)+.+(1+1/255)
=8+1/3+1/15+1/63+1/99+1/143+1/195+1/255
=8+0.5*(1-1/3)+0.5*(1/3-1/5)+0.5*(1/5-1/7)+.+0.5*(1/15-1/17)
=8+0.5（1-1/3+1/3-1/5+1/5-1/7+.+1/15-1/17）
=8+0.5*16/17
=144/17