1*2*3+2*4*6……+100*200*300/2*3*4+4*6*8……+200*300*400
=(1*2*3+2*2*2*1*2*3+.+100*100*100*1*2*3)/(2*3*4+2*2*2*2*3*4+.+100*100*100*2*3*4)
=1*2*3/2*3*4*[(1+2*2*2+...+...+100*100*100)/(1+2*2*2+.+100*100*100)]
=1*2*3/2*3*4
=1/4
1*2*3+2*4*6……+100*200*300/2*3*4+4*6*8……+200*300*400
=(1*2*3+2*2*2*1*2*3+.+100*100*100*1*2*3)/(2*3*4+2*2*2*2*3*4+.+100*100*100*2*3*4)
=1*2*3/2*3*4*[(1+2*2*2+...+...+100*100*100)/(1+2*2*2+.+100*100*100)]
=1*2*3/2*3*4
=1/4