Here is a lazy person's way of summing up your sequence. You could have done the same thing?
1+2-3-4+5+6-7-8+9+10-11-12+13+14-15-16+17+18-19-20+21+22-23-24+25+26-27-28+29+30-31-32+33+34-35-36+37+38-39-40+41+42-43-44+45+46-47-48+49+50-51-52+53+54-55-56+57+58-59-60+61+62-63-64+65+66-67-68+69+70-71-72+73+74-75-76+77+78-79-80+81+82-83-84+85+86-87-88+89+90-91-92+93+94-95-96+97+98-99-100 = - 100
