已知1+2+3·······+31+32+33=17乘33,求1-3+2-6+3-9+········+31-93+32-96+33-99的值,

1-3+2-6+3-9+……+31-93+32-96+33-99
=1+2+3……+31+32+33-(3+6+9+……+99)
=1+2+3……+31+32+33-3*(1+2+3……+31+32+33)
=(1-3)*(1+2+3……+31+32+33)
=-2*(1+2+3……+31+32+33)
=-2*17*33
=-1122

(1)求和公式:(首项+末项)*项数/2
项数=(末项-首项)/公差+1
(99-3)/3+1=33
3+6+9+…+93+96+99=(3+99)*33/2=51*33
1+2+3+......+33=17*33
1-3+2-6+3-9+4-12+...+31-93+32-96+33-99=17*33-51*33=-34*33=-1122
(2)3+6+9+…+93+96+99=3*(1+2+3+......+33)=3*17*33
1-3+2-6+3-9+4-12+...+31-93+32-96+33-99=17*33-3*17*33=-2*17*33=-1122

1-3+2-6+3-9+········+31-93+32-96+33-99
=1+2+3+····+33-(3+6+9+····+99)
=1+2+3+····+33-3*(1+2+3+····+33)
=-2*(1+2+3+····+33)
=-2*17*33