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\(A=\frac{9}{1.2}+\frac{9}{2.3}+\frac{9}{3.4}+...+\frac{9}{98.99}+\frac{9}{99.100}\)
\(A=\frac{1}{9}.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\right)\)
\(A=\frac{1}{9}.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)
\(A=\frac{1}{9}.\left(1-\frac{1}{100}\right)\)
\(A=\frac{1}{9}.\frac{99}{100}\)
\(A=\frac{11}{100}\)
A = 9/1.2 + 9/2.3 + 9/3.4 +...+ 9/98.99 + 9/99.100
= 9. (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/98 - 1/99 + 1/99 - 1/100)
= 9. (1 - 1/100)
= 9 . 99/100
= 891/100
![](https://rs.olm.vn/images/avt/0.png?1311)
Gọi A là biểu thức ta có:
A = 1.2+2.3+3.4+......+99.100
Gấp A lên 3 lần ta có:
A . 3 = 1.2.3 + 2.3.3 + 3.4.3 + … + 99.100.3
A . 3 = 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98)
A . 3 = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100
A . 3 = 99.100.101
A = 99.100.101 : 3
A = 33.100.101
A = 333 300
k cho mk nha pạn
ủng hộ mk nha mấy pạn khác
cảm ơn nhiều
Gọi A là biểu thức ta có:
A = 1.2+2.3+3.4+......+99.100
Gấp A lên 3 lần ta có:
A . 3 = 1.2.3 + 2.3.3 + 3.4.3 + … + 99.100.3
A . 3 = 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98)
A . 3 = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100
A . 3 = 99.100.101
A = 99.100.101 : 3
A = 33.100.101
A = 333 300
k cho mk nha pạn
ủng hộ mk nha mấy pạn khác
cảm ơn nhiều
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có : B = 1.2 + 2.3 + 3.4 + ... + 99.100
=> 3B = 1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3
=> 3B = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 99.100.(101 - 98)
=>3B = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100
=> 3B = 99.100.101
=> 3B = 999900
=> B = 333300
Vậy B = 333300
Bài làm :
Ta có :
B= 1.2 + 2.3 + 3.4 + ...+ 99.100
=>3B = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3
<=>3B= 1.2.3+2.3(4-1)+3.4(5-2)+...+98.99(100-97)+99.100(101-98)
<=>3B= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...-97.98.99+99.100.101-98.99.100
<=>3S = 99.100.101
<=> 3S = 999900
<=> B = 999900 : 3 = 333300
Vậy B = 333300
![](https://rs.olm.vn/images/avt/0.png?1311)
=9.(1/1.2+1/2.3+1/3.4+...+1/98.99+1/99.100)
=9.(1/1-1/2+1/2-1/3+1/3-1/4+....+1/98-1/99+1/99-1/100)
=9.(1/1-1/100)
=9-9/100
=891/100
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A = 1.2 + 2.3 + 3.4 + ... + 99.100
3A = 1.2.(3-0) + 2.3.(4-1) + 3.4.(5-2) + ... + 99.100.(101-98)
3A = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100
3A = 99.100.101
A = 33.100.101
A = 333300
\(A=1.2+2.3+3.4+4.5+...+97.98+98.99+99.100\)
\(3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+4.5.\left(6-3\right)+...+99.100.\left(101-98\right)\)
\(3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+...+99.100.101-98.99.100\)
\(3A=99.100.101\)
\(A=\frac{99.100.101}{3}=\frac{999900}{3}=333300\)
![](https://rs.olm.vn/images/avt/0.png?1311)
3A=1.2.3+2.3.(4-1)+.............+98.99.(100-97)+99.100.(101-98)
3A=1.2.3+2.3.4-1.2.3+...........+98.99.100-97.98.99+99.100.101-98.99.100
3A=99.100.101
A=99.100.101:3
A=333300
Ta có : 3A = 1.2.3 + 2.3.3 + 3.4.3 + .... + 98.99.3 + 99.100.3
=> 3A = 1.2.( 3 - 0 ) + 2.3.( 4 - 1 ) + 3.4.( 5 - 2 ) + ..... + 98.99.( 100 - 97 ) + 99.100.( 101 - 98 )
=> 3A = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ..... + 98.99.100 - 97.98.99 + 99.100.101 - 98.99.100
=> 3A = ( 1.2.3 + 2.3.4 + 3.4.5 + ..... + 98.99.100 + 99.100.101 ) - ( 0.1.2 + 1.2.3 + 2.3.4 + ..... + 98.99.100 )
=> 3A = 99.100.101 - 0.1.2
=> 3A = 99.100.101
=> A = 33.100.101
=> A = 333300
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A= 1.2 + 2.3 + 3.4 + ...+ 99.100
3A = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3
3A= 1.2.3+2.3(4-1)+3.4(5-2)+...+98.99(100-97)+99.100(101-98)
3A= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...-97.98.99+99.100.101-98.99.100
3A = 99.100.101 3S = 3.33.100.101
A=33.100.101= 333300
A= 1.2 + 2.3 + 3.4 + ...+ 99.100
3A = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3
3A= 1.2.3+2.3﴾4‐1﴿+3.4﴾5‐2﴿+...+98.99﴾100‐97﴿+99.100﴾101‐98﴿
3A= 1.2.3+2.3.4‐1.2.3+3.4.5‐2.3.4+...‐97.98.99+99.100.101‐98.99.100
3A = 99.100.101 3S = 3.33.100.101
A=33.100.101= 333300
Gọi A là biểu thức ta có:
A = 1.2+2.3+3.4+......+99.100
Gấp A lên 3 lần ta có:
A . 3 = 1.2.3 + 2.3.3 + 3.4.3 + … + 99.100.3
A . 3 = 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98)
A . 3 = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100
A . 3 = 99.100.101
A = 99.100.101 : 3
A = 33.100.101
A = 333 300
=333300