被除数=(101-100)(101+100)+……+(2-1)(2+1)
=1×(101+100)+……+1×(2+1)
=101+100+……+2+1
=(101+1)+(100+2)+……+(52+50)+51
=102×50+51
=(103-1)×50+51
=103×50-1×50+51
=103×50+1
所以余数是1