1-3+5-7+9-11+.+4997-4999=?

题目

1-3+5-7+9-11+.+4997-4999=?
1/3-7/12+9/20-11/30+13/42-15/56=?

答案

1-3+5-7+9-11+.+4997-4999
=(1-3)+(5-7)+(9-11)+...+(4997-4999)
=-2+(-2)+(-2)+...+(-2)
=-2×[(4997-1)÷4+1]
=-2×1250
=-2500;

1/3-7/12+9/20-11/30+13/42-15/56
=1/3-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+(1/6+1/7)-(1/7+1/8)
=1/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7-1/8
=-1/8;
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