A=1/2×(4/1×5+6/5×11+8/11×19+12/29×41
=1/2×(1/1-1/5+1/5-1/11+1/11-1/19+1/29-1/41)
=1/2×(1/1+1/29-1/41)
=1/2+1/58-1/82
=1189/2378+41/2378-29/2378
=1201/2378>1189/2378=1/2> 1/3
=>1201/2378>1/3
B=1/1×4+2/4×10+3/10×19+4/19×31
=1/3×(3/1×4+2/4×10+3/10×19+12/19×31)
=1/3×(1/1-1/4+1/4-1/10+1/10-1/19+1/19-1/31)
=1/3×(1/1-1/31)
=1/3×30/31
=30/91<30/90=1/3
=>30/91<1/3
có 1201/2378>1/3
30/91<1/3
=>1201/2378>1/3>30/91
=>1201/2378>30/91
=>A>B