(-1)+(+2)+(-3)+(+4)+...+(-2007)+(+2008+(-2009+(+2010)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/10 16:16:19
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(-1)+(+2)+(-3)+(+4)+...+(-2007)+(+2008+(-2009+(+2010)
(-1)+(+2)+(-3)+(+4)+...+(-2007)+(+2008+(-2009+(+2010)
(-1)+(+2)+(-3)+(+4)+...+(-2007)+(+2008+(-2009+(+2010)
原式=-(1+3+5+7+.2009)+(2+4+6+8+.2010)
=-1010025+1011030
=1005
也可以
原式=(-1+2)+(-3+4)+(-5+6)+.+(-2009+2010)
=1*1005
=1005
每两项相加得
1+1+1+。。。+1
=1005
(-1)+(+2)+(-3)+(+4)+...+(-2007)+(+2008)+(-2009)+(+2010)
=(-1+2)+(-3+4)+...+(-2007+2008)+(-2009+2010)
=1+1+1+...+1+1 (注:2010个数,两个数一组,共2010/2=1005组)
=1005
两个一组,和为1
(-1)+(+2)=1
(-3)+(+4)=1
.......
(-2007)+(+2008)=1
(-2009+(+2010)=1
(-1)+(+2)+(-3)+(+4)+...+(-2007)+(+2008+(-2009+(+2010)
=1x2010/2
=1005
每两项相加=1+1+1+...+1共有2010/2=1005项。∴原式=1005