1/3+1/(3+6)+1/(3+6+9)+...+1/(3+6+9+...+99)
=1/3+1/[3*(1+2)]+1/[3*(1+2+3)]+...+1/[3*(1+2+3+...+33)]
=2/3*[1/(1*2)+1/(2*3)+1/(3*4)+...+1/(33*34)]
=2/3*[1-1/2+1/2-1/3+1/3-1/4+...+1/33-1/34]
=2/3*[1-1/34]
=11/17
1/3+1/(3+6)+1/(3+6+9)+...+1/(3+6+9+...+99)
=1/3+1/[3*(1+2)]+1/[3*(1+2+3)]+...+1/[3*(1+2+3+...+33)]
=2/3*[1/(1*2)+1/(2*3)+1/(3*4)+...+1/(33*34)]
=2/3*[1-1/2+1/2-1/3+1/3-1/4+...+1/33-1/34]
=2/3*[1-1/34]
=11/17