1-2+3-4+5-6+7-8···-1998+1999=1000 计算过程是什么?重谢!

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1-2+3-4+5-6+7-8···-1998+1999=1000 计算过程是什么?重谢!

1-2+3-4+5-6+7-8···-1998+1999=1000 计算过程是什么?重谢!
1-2+3-4+5-6+7-8···-1998+1999=1000 计算过程是什么?重谢!

1-2+3-4+5-6+7-8···-1998+1999=1000 计算过程是什么?重谢!
(1-2)+(3-4)+(5-6)+……(1997-1998)+1999
=-1+ -1+ -1 +……+ -1 + 1999
=-999+1999
=1000

原式=(1+1999)*1000/2-(2+1998)*999/2=1000

-2+3,-4+5。。。都等于1
以此类推-1998+1999=1
总共是999个一,再加上前面的第一个1
所以=1000

(1+1999)-(2+1998)+(3+1997)-(4+1996)+..+(499+501)-1000=1000

1-2+3-4+5-6+7-8···-1998+1999
=1+(-2+3)+(-4+5)+(-6+7)+(-8+9)···(-1998+1999)
=1+1+1+...+1
=1*1000
=1000

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