1/1*3+1/2*4+1/3*5+--+1/20*22
=1/2（1/1-1/3）+1/2（1/2-1/4）+1/2（1/3-1/5）+1/2(1/4-1/6)+---+1/2(1/20-1/22)
=1/2(1/1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+-----+1/19-1/21+1/20-1/22)
=1/2( 1/1+1/2-1/21-1/22)
=1/2(3/2-43/462)
=1/2(693/462-43/462)
=1/2 * 650/462
=325/462