计算(+1)+(-2)+(+3)+(-4)+······+(-100)+(+101)+(-102)
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计算(+1)+(-2)+(+3)+(-4)+······+(-100)+(+101)+(-102)
计算(+1)+(-2)+(+3)+(-4)+······+(-100)+(+101)+(-102)
计算(+1)+(-2)+(+3)+(-4)+······+(-100)+(+101)+(-102)
(+1)+(-2)+(+3)+(-4)+······+(-100)+(+101)+(-102)
=(1-2)+(3-4)+...+(101-102)
=(-1)+(-1)+...+(-1)
=(-1)*51
=-51
(+1)+(-2)+(+3)+(-4)+······+(-100)+(+101)+(-102)
=(-1)*51=-51
(+1)+(-2)+(+3)+(-4)+······+(-100)+(+101)+(-102)
=[+1+(-2)]+[(+3)+(-4)]+……+[(+99)+(-100)]+[(+101)+(-102)]
=(-1)+(-1)+……+(-1)+(-1)
=(-1)×(102÷2)
=(-1)×51
=-51
1-2+3-4+5-6.......+101-102=-51
=(1+3+5+7+...+101)-(2+4+...+100+102)
1+3+5+7+...+101为 102*51/2=2601(高斯定理)
2+4+...+100+102为104*51/2=2652
所以
=(1+3+5+7+...+101)-(2+4+...+100+102)=2601-2652=-51
原式=1-2+3-4+5-6......+101-102
=(-1)+(-1).....+(-1)
=(-1)*51
=-51
两种方法:
1.
(+1)+(-2)+(+3)+(-4)+······+(-100)+(+101)+(-102)
=[+1+(-2)]+[(+3)+(-4)]+……+[(+99)+(-100)]+[(+101)+(-102)]
=(-1)+(-1)+……+(-1)+(-1)
=(-1)×(102÷2)
=(-1)×51
=-51
2....
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两种方法:
1.
(+1)+(-2)+(+3)+(-4)+······+(-100)+(+101)+(-102)
=[+1+(-2)]+[(+3)+(-4)]+……+[(+99)+(-100)]+[(+101)+(-102)]
=(-1)+(-1)+……+(-1)+(-1)
=(-1)×(102÷2)
=(-1)×51
=-51
2.用等差数列的方法
1+3+5+7+9+······+101+(-2-4-6-······-102)=(1+101)*51/2-(2+4+6+······+102)=(1+101)*51/2-(2+102)*51/2=(1-2+101-102)*51/2=-2*51/2=-51
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