99999²+199999 1986+1988+1990+…+2000分之1985+1987+1989+…+1999的简便算法
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解决时间 2021-02-08 12:11
- 提问者网友：回忆在搜索
- 2021-02-08 05:58
99999²+199999 1986+1988+1990+…+2000分之1985+1987+1989+…+1999的简便算法
最佳答案
- 五星知识达人网友：我住北渡口
- 2021-02-08 06:59
99999²+199999
=99999²+199998+1
=99999²+2*99999+1
=(99999+1)²
=100000²
=10000000000
(1985+1987+1989+…+1999)/(1986+1988+1990+…+2000)
=[(1985+1999)*8/2]/[(1986+2000)*8/2]
=1992/1993
=99999²+199998+1
=99999²+2*99999+1
=(99999+1)²
=100000²
=10000000000
(1985+1987+1989+…+1999)/(1986+1988+1990+…+2000)
=[(1985+1999)*8/2]/[(1986+2000)*8/2]
=1992/1993
全部回答
- 1楼网友：枭雄戏美人
- 2021-02-08 08:07
(1985+1987+1989+……+1999)/(1986+1988+1990+……+2000)=
（1986-1+1988-1……+2000-1）/(1986+1988+1990+……+2000)=
{(1986+1988+1990+……+2000)-8}/(1986+1988+1990+……+2000)=
1-8/(1986+1988+1990+……+2000)=1-8/15944
=1-1/1993
=1992/1993
（1986-1+1988-1……+2000-1）/(1986+1988+1990+……+2000)=
{(1986+1988+1990+……+2000)-8}/(1986+1988+1990+……+2000)=
1-8/(1986+1988+1990+……+2000)=1-8/15944
=1-1/1993
=1992/1993
- 2楼网友：你可爱的野爹
- 2021-02-08 07:58
99999²+199999
=99999²+99999+100000
=99999*(99999+1)+100000
=99999*100000+100000
=(99999+1)*100000
=10000000000
1986+1988+1990+…+2000分之1985+1987+1989+…+1999
=(1986-1+1988-1+1990-1+...+2000-1)/(1986+1988+1990+…+2000)
=(1986+1988+1990+…+2000-8)/(1986+1988+1990+…+2000)
=1-8/[8*(1986+2000)/2]
=1-1/1993
=1992/1993
=99999²+99999+100000
=99999*(99999+1)+100000
=99999*100000+100000
=(99999+1)*100000
=10000000000
1986+1988+1990+…+2000分之1985+1987+1989+…+1999
=(1986-1+1988-1+1990-1+...+2000-1)/(1986+1988+1990+…+2000)
=(1986+1988+1990+…+2000-8)/(1986+1988+1990+…+2000)
=1-8/[8*(1986+2000)/2]
=1-1/1993
=1992/1993
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