数学计算题(急用!)2000-1990+1980-1970+...+20-10————————————————-------------------------------(1-1/2)*(1-1/3)*(1-1/4)*...*(1-1/999)*(1-1/1000)[请写出过程,不用写太长](1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4) [上面一道,用简便~]1*2+2*4+3*6+...+1002*2004 ---
2019-04-02
数学计算题(急用!)
2000-1990+1980-1970+...+20-10
————————————————-------------------------------
(1-1/2)*(1-1/3)*(1-1/4)*...*(1-1/999)*(1-1/1000)
[请写出过程,不用写太长]
(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4)
[上面一道,用简便~]
1*2+2*4+3*6+...+1002*2004
----------------------------------
1*5+2*10+3*15+...+1002*5010
优质解答
1,
可以看出这个式子是2000/10=200个
两个数一组,共200/2=100组
每组是20-10=10或2000-1990=10
列式子：10＊（2000／20／2）＝1000
2,
(1-1/2)*(1-1/3)*(1-1/4)*...*(1-1/999)*(1-1/1000)
＝1／2＊2／3＊3／4＊...*998/999*999/1000
=1/1000
如果你上面的是一道题：答案就是1000/（1/1000）=1000000
3,
(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4)
=(1+1/2+1/3+1/4)*(1+1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4)
= (1+1/2+1/3+1/4+1/5)*[(1+1/2+1/3+1/4)-(1/2+1/3+1/4)]-(1+1/2+1/3+1/4)
=(1+1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4)
=1/5
附加题
1*2+2*4+3*6+...+1002*2004
----------------------------------
1*5+2*10+3*15+...+1002*5010
=2*（1*1+2*2+3*3+...+1002*1002)
-----------------------------
5*(1*1+2*2+3*3+...+1002*1002)
=2/5
1,
可以看出这个式子是2000/10=200个
两个数一组,共200/2=100组
每组是20-10=10或2000-1990=10
列式子：10＊（2000／20／2）＝1000
2,
(1-1/2)*(1-1/3)*(1-1/4)*...*(1-1/999)*(1-1/1000)
＝1／2＊2／3＊3／4＊...*998/999*999/1000
=1/1000
如果你上面的是一道题：答案就是1000/（1/1000）=1000000
3,
(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4)
=(1+1/2+1/3+1/4)*(1+1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4)
= (1+1/2+1/3+1/4+1/5)*[(1+1/2+1/3+1/4)-(1/2+1/3+1/4)]-(1+1/2+1/3+1/4)
=(1+1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4)
=1/5
附加题
1*2+2*4+3*6+...+1002*2004
----------------------------------
1*5+2*10+3*15+...+1002*5010
=2*（1*1+2*2+3*3+...+1002*1002)
-----------------------------
5*(1*1+2*2+3*3+...+1002*1002)
=2/5