1-2+3-4+5-6+...+97-98+99+100
1+2-3+4+5-6+7+8-9...+97+98-99
人气:293 ℃ 时间:2020-02-15 10:01:01
解答
1-2+3-4+5-6+...+97-98+99+100
=100+(99-98)+(97-96)+(95-94)+...+(3-2)+1(倒排,加括号)
=100+1+...+1
=150
1+2-3+4+5-6+7+8-9...+97+98-99
=(1+2-3)+(4+5-6)+(7+8-9)...+(97+98-99)(加括号)
=0+3+6+9+...+96
=3*(1+2+3+...+32)
=3*32*(1+32)/2(倒排相加处以2)
=1584
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