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![](https://rs.olm.vn/images/avt/0.png?1311)
đạt A= 1.2 + 2.3 + 3.4 +.............+ 98.99
3A=1.2.3+2.3.3+.....+98.99.3
3A=1.2.3+2.3.4-2.3.1+.....+98.99.100-99.98.97
3A=98.99.100
A=98.33.100
![](https://rs.olm.vn/images/avt/0.png?1311)
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
![](https://rs.olm.vn/images/avt/0.png?1311)
B = 1.2 + 3.4 + 5.6 +...+ 98.99
3B = 1.2(3-0) + 2.3(4-1) ...... 98.99 (100-97)
3B = 1.2.3-0.2.3.4-1 ......... 98.99.100-97
3B = ( 1.2.3+2.3.4+.....+98.99.100) - ( 0.1.2+ 1.2.3+.... + 97.98.99)
3B = 98.99.100
3B = 970200
B = 323400
![](https://rs.olm.vn/images/avt/0.png?1311)
C=1*2+2*3+3*4+...+98*99
C=2+6+12+...+9702
C=2+9702
C=9704
vay C=9704
D=(1*99+2*99+3*99+...+99*99)-(1*2+2*3+3*4+...+98*99)
D=(99+198+297+...+9801)-(2+6+12+...+9702)
D=(99+9801)-(2+9702)
D=9900-9704
D=196
vay D=196
ai di qua dong tinh thi nho h cho minh nhe
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: \(A=1.2+2.3+...+98.99\)
\(\Rightarrow3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+98.99.\left(100-97\right)\)
\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+98.99.100-97.98.99\)
\(\Rightarrow3A=98.99.100\)
\(\Rightarrow A=\frac{98.99.100}{3}\)
\(\Rightarrow A=98.33.100\)
\(\Rightarrow A=323400\)
A=1.2+2.3+3.4+........+98.99
3A=1.2.3+2.3.3+3.4.3+........+98.99.3
3A=1.2.3+2.3.(4 -1) +3.4.(5 -2)+........+98.99.(100 -97)
3A=1.2.3+2.3.4 -1.2.3 +3.4.5 -2.3.4 +........+98.99.100 -97.98.99
3A=98.99.100
===>A=(98.99.100)/3
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{98.99}+\frac{2}{99.100}\)
= \(2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\right)\)
= \(2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)
= \(2\left(1-\frac{1}{100}\right)\)
=\(2.\frac{99}{100}\)
=\(\frac{99}{50}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Số các số hạng của A là :
( 99 - 1 ) : 1 + 1 = 99 ( số )
Tổng A là :
( 99 + 1 ) . 99 : 2 = 4950
Vậy tổng A = 4950 .
![](https://rs.olm.vn/images/avt/0.png?1311)
BÀI 1:
\(S=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(S=1+\frac{1}{1.2}+\frac{1}{2.2}+\frac{1}{2.4}+\frac{1}{4.4}+\frac{1}{4.8}\)
\(S=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}\)
\(S=1+1-\frac{1}{8}\)
\(S=\frac{15}{8}\)
BÀI 2:
\(A=1.2+2.3+3.4+...+98.99\)
\(\Rightarrow3A=1.2.3+2.3.3+3.4.3+...+98.99.3\)
\(3A=1.2.\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+98.99.\left(100-97\right)\)
\(3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+98.99.100-97.98.99\)
\(3A=\left(1.2.3+2.3.4+3.4.5+98.99.100\right)-\left(1.2.3+2.3.4+...+97.98.99\right)\)
\(3A=98.99.100\)
\(3A=970200\)
\(\Rightarrow A=970200:3\)
\(A=323400\)
CHÚC BN HỌC TỐT!!!
![](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