a. \(\left(\dfrac{1}{3}+\dfrac{2}{3}\right)+\dfrac{3}{4}=1+\dfrac{3}{4}=\dfrac{7}{4}\)

b. \(\dfrac{3}{4}+\dfrac{3}{5}+\dfrac{2}{8}+\dfrac{4}{10}=\left(\dfrac{3}{4}+\dfrac{2}{8}\right)+\left(\dfrac{3}{5}+\dfrac{4}{10}\right)=1+1=2\)

 a ) `1/3 + 3/4 + 2/3 + 1/4 `

 `= (1/3 + 2/3 )+ (3/4 + 1/4)`

 `=         1          +        1  `

 `=                    2

b 3/4 + 3/5 + 2 phần 8 + 4/10` 

`= (3/4 + 2/8 ) + ( 3/5 + 4/10 ) `

`=       1          +     1 `

`=             2`

=2666666000

Có công thức như sau

1x2+2x3+3x4+...+nx(n+1)=nx(n+1)x(n+2):3

phần sau thì sao

\(\frac{3}{1}+\frac{3}{1+2}+\frac{3}{1+2+3}+...+\frac{3}{1+2+...+100}\)

\(=3\left(\frac{1}{\frac{1\cdot2}{2}}+\frac{1}{\frac{2\cdot3}{2}}+\frac{1}{\frac{3\cdot4}{2}}+...+\frac{1}{\frac{100\cdot101}{2}}\right)\)

\(=3\left(\frac{2}{1\cdot2}+\frac{2}{2\cdot3}+...+\frac{2}{100\cdot101}\right)\)

\(=6\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{100\cdot101}\right)\)

\(=6\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{100}-\frac{1}{101}\right)\)

\(=6\left(1-\frac{1}{101}\right)=6-\frac{6}{101}=\frac{606-6}{101}=\frac{600}{101}\)

1)=90

2)=8330

3)=10

Ai kết bạn với mk mk cho 3 tích lun

A=1+3+3^2+3^3+3^4

=1+3+9+27+81

=(9+81)+(3+27)+1

=90+30+1

=121

B=(3^2+1)×(3^4+1)×(3^8+1)

=(9+1)×(81+1)×(6561+1)

=10x82x6562

=820x6562

=5380840

A =1+3+3²+3³+3⁴

3A =3+3²+3³+3⁵

3A-A=3⁵-1

2A =243-1

A=242:2

A=121

Ta có: 

\(A=\frac{1}{3}-\frac{1}{3^2}+\frac{1}{3^3}-\frac{1}{3^4}+...+\frac{1}{3^{99}}-\frac{1}{3^{100}}\)

=> \(3A=1-\frac{1}{3}+\frac{1}{3^2}-\frac{1}{3^3}+...+\frac{1}{3^{98}}-\frac{1}{3^{99}}\)

=> \(A+3A=1-\frac{1}{3^{100}}\)

=> \(4A=\frac{3^{100}-1}{3^{100}}\)

=> \(A=\frac{3^{100}-1}{4.3^{100}}\)