解:1-1/2+1/3-1/4+…+1/n-1 -1/n=1/2+1/12+1/20+1/30+...+1/n(n-1)=1/1*2+1/3*4+1/4*5+1/5*6+...+1/n(n-1)=1-1/2+1/2-1/3+1/3-1/4+...+1/(n-1)-1/n=1-1/n=(n-1)/n
