1.1/1=1;1+1/(1+2)=4/3;4/3+1/(1+2+3)=3/2;(6/4)3/2+1/(1+2+3+4)=8/5;猜想1/1+...+1/(1+...+n)=(2n)/(n+1)2.n=1时成立.假设n=k时成立；n=k+1时,1/1+...+1/(1+...+(n+1))=2n/(n+1)+1/((1+(n+1))(n+1)/2)