1/5×1/6+1/6×1/7+1/7×1/8+1/8×1/9+1/9×1/10这道题用简便方法怎样做?

问题描述:

1/5×1/6+1/6×1/7+1/7×1/8+1/8×1/9+1/9×1/10这道题用简便方法怎样做?
带解析.用简便方法怎样做?有什么类似的题吗?

1/5×1/6=1/5-1/6,1/6×1/7=1/6-1/7,1/7×1/8=1/7-1/8,1/8×1/9=1/8-1/91/9×1/10=1/9-1/101/5×1/6+1/6×1/7+1/7×1/8+1/8×1/9+1/9×1/10=1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10=1/5-1/10=2/10-1/10=1/10...为什么1/n(n+1)=1/n-1/(n+1)呢?还是有些不懂……因为(1/n)-1/(n+1)=(n+1)/[n(n+1)]-n/[n(n+1)]---------通分=[(n+1)-n]/[n(n+1)]=1/[n(n+1)]1/[n(n+1)]=(1/n)-1/(n+1)假设取个特殊值,n=3,也就是1/(3×4)=1/3-1/4有疑问欢迎继续追问,祝学习进步!