1+1/1+2+1/1+2+3+.+1/1+2+3+.+100=的过程与解答

1+2+3+……+n=n*(n+1)/2 n=1,2,……
1/(1+2+3+……+n)=2/[n*(n+1)]
1+1/(1+2)+1/(1+2+3)+……+1/(1+2+3+……+100)
=1+2/(2*3)+2/(3*4)+……+2/(100*101)
=2*(1-1/2+1/2-1/3+1/3-1/4+……+1/100-1/101)
=2*(1-1/101)
=200/101