已知 1+2+3+4+5+...+31+32+33=17*33 求1-3+2-6+3-9+4-12+...+31-96+33-99 的值 (+1)+(-2)+(-3)+(-4)……+(+2005)+(-2006)+2007
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/27 07:18:29
![已知 1+2+3+4+5+...+31+32+33=17*33 求1-3+2-6+3-9+4-12+...+31-96+33-99 的值 (+1)+(-2)+(-3)+(-4)……+(+2005)+(-2006)+2007](/uploads/image/z/588533-5-3.jpg?t=%E5%B7%B2%E7%9F%A5+1%2B2%2B3%2B4%2B5%2B...%2B31%2B32%2B33%3D17%2A33+%E6%B1%821-3%2B2-6%2B3-9%2B4-12%2B...%2B31-96%2B33-99+%E7%9A%84%E5%80%BC+%28%2B1%29%2B%28-2%29%2B%28-3%29%2B%28-4%29%E2%80%A6%E2%80%A6%2B%28%2B2005%29%2B%28-2006%29%2B2007)
已知 1+2+3+4+5+...+31+32+33=17*33 求1-3+2-6+3-9+4-12+...+31-96+33-99 的值 (+1)+(-2)+(-3)+(-4)……+(+2005)+(-2006)+2007
已知 1+2+3+4+5+...+31+32+33=17*33 求1-3+2-6+3-9+4-12+...+31-96+33-99 的值
(+1)+(-2)+(-3)+(-4)……+(+2005)+(-2006)+2007
已知 1+2+3+4+5+...+31+32+33=17*33 求1-3+2-6+3-9+4-12+...+31-96+33-99 的值 (+1)+(-2)+(-3)+(-4)……+(+2005)+(-2006)+2007
1-3+2-6+3-9+4-12+...+31-96+33-99
=(1+2+3+4+5+...+31+32+33)-(3+6+9+...+96+99)
=17*33-3*(1+2+3+4+5+...+31+32+33)
=17*33-3*17*33
=(1-3)17*33
=-2*17*33
(+1)+(-2)+(-3)+(-4)……+(+2005)+(-2006)+2007这题你好好检查一下,是不是题目写错了,
分开求,原式等于1+2+3+4……+33-3x(1+2+3+4……+33)=17x33-3x17x33就行了
1-3+2-6+3-9+4-12+...+31-96+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
= -1122
(+1)+(-2)+(-3)+(-4)……+(+2005)+(-2006)+2007<...
全部展开
1-3+2-6+3-9+4-12+...+31-96+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
= -1122
(+1)+(-2)+(-3)+(-4)……+(+2005)+(-2006)+2007
=1-2+3-4+5-6+……+2005-2006+2007
=(1-2)+(3-4)+(5-6)+……+(2005-2006)+2007
= -1-1-1-……-1+2007
=-1003+2007
=1004
收起
1-3+2-6+3-9+4-12+...+31-96+33-99
=(1+2+3+4+5+...+31+32+33)-(3+6+9+...+96+99)
=17*33-3*(1+2+3+4+5+...+31+32+33)
=17*33-3*17*33
=(1-3)17*33
=-2*17*33
(+1)+(-2)+(-3)+(-4)……+(+2005)+(-2006)+2007