1/19*21+1/21*23+.+1/99*101
=1/2(1/19-1/21)+1/2(1/21-1/23)+.+1/2(1/99-1/101)
=1/2(1/19-1/21+1/21-1/23+.-1/99+1/99-1/101)
=1/2(1/19-1/101)
=1/38-1/202