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![](https://rs.olm.vn/images/avt/0.png?1311)
= (1+3+....+999).(25.4.111-25.4.111)
= (1+3+....+999).0
= 0
Tk mk nha
=(1+3+5+...+999).(25.4.111-25.4.111)
=(1+3+5+...+999).0
=0
chúc bạn học tốt
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có: A=\(\frac{9}{99.100}+\frac{9}{100.101}+....+\frac{9}{2018.1019}\)
=>A=\(9.\left(\frac{1}{99.100}+\frac{1}{100.101}+....+\frac{1}{2018.2019}\right)\)
=>A=\(9.\left(\frac{1}{99}-\frac{1}{100}+\frac{1}{100}-\frac{1}{101}+...+\frac{1}{2018}-\frac{1}{2019}\right)\)
=>A=\(9.\left(\frac{1}{99}-\frac{1}{2019}\right)\)
=>A=\(9.\frac{640}{66627}\)
=>A=\(\frac{640}{7403}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
B = 1*1 + 2*2 + 3*3 + ... + 199*199
B = ( 1+ 2 + 3 +...+ 199 ) * ( 1 + 2 + 3 +...+ 199 )
B = 19900 * 19900
B = 19900 * 2
B = 39800
Chắc là vậy đó bạn :)
B= 1.1+2.2+3.3+...+199.199
B= 1.(2-1)+2.(3-1)+3.(4-1)+...+199.(200-1)
B=1.2-1+2.3-2+3.4-3+...+199.200-199
B=(1.2+2.3+3.4+...+199.200)(Đặt là M)-(1+2+3+...+199)(Đặt là N)
M= 1.2+2.3+3.4+...+199.200
3M=1.2.3+2.3.3+3.4.3+...+199.200.3
3M=1.2.3+2.3.(4-1)+3.4.(5-2)+...+199.200.(201-198)
3M=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+199.200.201-199.200.198
3M=199.200.201
M= 199.200.201:3
M=2666600
N= 1+2+...199.Có: 199 số hạng
N= (199+1).199:2=19900
Thấy B= M-N
=> B= 2666600-19900=2646700
![](https://rs.olm.vn/images/avt/0.png?1311)
=1*200+2*(200-1)+3*(200-2)+...+199(200-198)+200(200-199)
=(1+2+3+...+200)-(1*2+2*3+...+199*200)
=200*201/2-199*200*201/3
=1353400
![](https://rs.olm.vn/images/avt/0.png?1311)
\(B=\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+....+\frac{198}{2}+\frac{199}{1}\)
\(=\left(\frac{1}{199}+1\right)+\left(\frac{2}{198}+1\right)+\left(\frac{3}{197}+1\right)+.....+\left(\frac{198}{2}+1\right)+\frac{200}{200}\)
\(=200\left(\frac{1}{100}+\frac{1}{199}+\frac{1}{198}+....+\frac{1}{2}\right)\)
= 200.A
=> A:B=\(\frac{1}{200}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
=1*200+2*(200-1)+3*(200-2)+...+199(200-198)+200(200-199)
=(1+2+3+...+200)-(1*2+2*3+...+199*200)
=200*201/2-199*200*201/3
=1353400
1234567654321
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