计算1-(1+2)+(1+2+3)-(1+2+3+4)+…-(1+2+…+98)+(1+2+…+99)=_.

问题描述:

计算1-(1+2)+(1+2+3)-(1+2+3+4)+…-(1+2+…+98)+(1+2+…+99)=______.

1+(1+2)+(1+2+3)-(1+2+3+4)+…-(1+2+…+98)+(1+2+…+99)
=1+{[(1+2+3)-(1+2)]+…[(1+2+…+99)-(1+2+…+98)]}
=1+49
=50
故答案为:50.