丨1/4-1/3丨＋丨1/5-1/4丨＋丨1/6-1/5丨＋…丨1/20-1/19丨

因为绝对值里的数,可以表示为1/n-1/(n+1)
所以1/n-1/(n+1)=(n+1)/n(n+1)-n/n(n+1)=1/n(n+1)>0
所以绝对值1/n-1/(n+1)=1/n-1/(n+1)
所以丨1-1/2丨+丨1/2-1/3丨+丨1/3-1/4丨+丨1/4-1/5丨+…丨1/9-1/10丨
=1-1/2+1/2-1/3+1/3+1/4+1/4+1/5+…1/9-1/10
=1+（-1/2+1/2）+（-1/3+1/3）+（-1/4+1/4）+（-1/5+…1/9）-1/10
=1-1/10
=9/10