答案是200/101
1+2+3+…n= (n+1)*n/2
1/(1+2+3+…n)=2/(n+1)*n
1+1/(1+2)+ 1/(1+2+3)+...+ 1/(1+2+3+…100)
=2/(1+1)*1 +2/(2+1)*2 +2/(3+1)*3...+ 2/(100+1)*100
=2/2*1 +2/3*2 +2/4*3...+ 2/101*100
=2{1/2*1 +1/3*2 +1/4*3...+1/101*100}
=2[(1/1-1/2)+ (1/2-1/3)+ (1/3-1/4)+.+ (1/100-1/101)]
=2[1-1/101]
=200/101