小学数学题,

来源:百度知道 编辑:UC知道 时间:2024/06/25 16:16:12
4/3+16/15+36/35+64/63+100/99+144/143+196/195+256/255

我帮你。。。首先跟你说1/(n(n+2))=(1/(n-1)-1/(n+2))/2
所以原式=8+1/(1*3)+1/(3*5)+1/(5*7)...+1/(15*17)
=8+(1/1-1/3+1/3-1/5+1/5-1/7...+1/15-1/17)/2
=8+8/17
=144/17
不明白的问我

无能为力

4/3+16/15+36/35+64/63+100/99+144/143+196/195+256/255
=1+1+1+1+1+1+1+1+1/3+1/15+1/35+1/63+1/99+1/143+1/195+1/255
=8+1/2(1-1/3+1/3-1/5+......+1/15-1/17)
=8+1/2(1-1/17)
=8又8/17

8+1/3+1/15+1/35+1/63+1/99+1/143+1/195+1/255
=8+1/3+1/2*{(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+....+(1/15-1/17)}
=8+1/3+1/2*(1/3-1/17)
=8+1/3+7/51
=8+8/17
也就是8又17分之8