\(\frac{2019}{1\times2}+\frac{2019}{2\times3}+\frac{2019}{3\times4}+...+\frac{2019}{2018\times2019}\)

\(=2019\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{2018\times2019}\right)\)

\(=2019\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2018}-\frac{1}{2019}\right)\)

\(=2019\left(1-\frac{1}{2019}\right)\)

\(=2019\left(\frac{2019}{2019}-\frac{1}{2019}\right)\)

\(=2019\times\frac{2018}{2019}\)\(=\frac{2019\times2018}{2019}=2018\)

a: =58(57+150-125)=58x82=4756

b: \(=9\cdot5-4\cdot7+83=45-28+83=100\)

c: =(2019-2019)+(-247-53)=-300

d: \(=13\cdot70-50\cdot\left[10:2+8\right]=910-50\cdot13=910-650=260\)

\(a,=58.\left(57+150-125\right)\\ =58.82=4756\\ b,=9.5-4.7+83.1\\ =45-28+83=100\)

a: Số cần tìm là 5,32:0,125=42,56

b: \(A=1+\dfrac{1}{2019}-1-\dfrac{1}{2018}+\dfrac{1}{2018}-\dfrac{1}{2019}=0\)

giá trị biểu thức là 174

Ta có x = 2018

=> x + 1 = 2019

\(x^5-2019.x^4+2019.x^3-2019.x^2+2019.x-2020\)

\(=x^5-\left(x+1\right).x^4+\left(x+1\right).x^3-\left(x+1\right).x^2+\left(x+1\right).x-2020\)

\(=x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x-2020\)

\(=x-2020\)

Thay x = 2018 vào biểu thức , ta được

\(2018-2020=-2\)

Vậy giá trị biểu thức là -2

Ta có : x³ + y³ = z(3xy - z²)

=> x³ + y³ = 3xyz - z³

=> x³ + y³ + z³ - 3xyz = 0

=> (x + y)(x² - xy + y²) + z³ - 3xyz = 0

=> (x + y)³ - 3xy(x + y) + z³ - 3xyz = 0

=> [(x + y)³ + z³] - 3xy(x + y) - 3xyz  = 0

=> (x + y + z)[(x + y)² - (x + y)z + z²] - 3xy(x + y + z) = 0

=> (x + y +z)(x² + y ² + 2xy - xz - yz + z²) - 3xy(x + y + z) = 0

=> (x + y + z)(x² + y² + z² - xy - yz - zx) = 0

=> x² + y² + z² - xy - yz - zx = 0 (Vì x + y + z = 3)

=> 2(x² + y² + z² - xy - yz - zx) = 0

=> 2x² + 2y² + 2z² - 2xy - 2yz - 2zx = 0

=> (x² - 2xy + y²) + (y² - 2yz + z²) + (x² - 2zx + z²) = 0

=> (x - y)² + (y - z)² + (x - z)² = 0

=> \(\hept{\begin{cases}x-y=0\\y-z=0\\x-z=0\end{cases}}\Rightarrow x=y=z\)

mà x + y + z = 3

=> x = y = z = 1

Khi đó A = 673(x²⁰¹⁹ + y²⁰¹⁹ + z²⁰¹⁹) + 1 

= 673(1²⁰¹⁹ + 1²⁰¹⁹ + 1²⁰¹⁹) + 1

= 673.3 + 1 = 2020

Vậy A = 2020

1. \(\dfrac{2019}{2020}-\left(\dfrac{2019}{2020}-\dfrac{2020}{2021}\right)\)

\(=\dfrac{2019}{2020}-\dfrac{2019}{2020}+\dfrac{2020}{2021}\)

\(=0+\dfrac{2020}{2021}=\dfrac{2020}{2021}\)

Giải:

1) \(\dfrac{2019}{2020}-\left(\dfrac{2019}{2020}-\dfrac{2020}{2021}\right)\)  

\(=\dfrac{2019}{2020}-\dfrac{2019}{2020}+\dfrac{2020}{2021}\) 

\(=\left(\dfrac{2019}{2020}-\dfrac{2019}{2020}\right)+\dfrac{2020}{2021}\) 

\(=0+\dfrac{2020}{2021}\) 

\(=\dfrac{2020}{2021}\) 

2) \(\dfrac{2}{9}+\dfrac{7}{9}:\left(\dfrac{42}{5}-\dfrac{7}{5}\right)\) 

\(=\dfrac{2}{9}+\dfrac{7}{9}:7\) 

\(=\dfrac{2}{9}+\dfrac{1}{9}\) 

\(=\dfrac{1}{3}\) 

3) \(\dfrac{3}{4}+\dfrac{x}{4}=\dfrac{5}{8}\) 

            \(\dfrac{x}{4}=\dfrac{5}{8}-\dfrac{3}{4}\) 

            \(\dfrac{x}{4}=\dfrac{-1}{8}\)  

\(\Rightarrow x=\dfrac{4.-1}{8}=\dfrac{-1}{2}\) 

4) \(\left|3x+1\right|-\dfrac{1}{4}=\dfrac{-1}{4}\) 

            \(\left|3x-1\right|=\dfrac{-1}{4}+\dfrac{1}{4}\) 

            \(\left|3x-1\right|=0\) 

             \(3x-1=0\) 

                    \(3x=0+1\) 

                    \(3x=1\) 

                      \(x=1:3\) 

                      \(x=\dfrac{1}{3}\) 

Chúc bạn học tốt!

1) 1/1.2 + 1/2.3 + ... + 1/6.7

= 1 - 1/2 + 1/2 - 1/3 + ... + 1/6 - 1/7

= 1 - 1/7

= 6/7

2) 1/2 + 1/6 + 1/12 + .. + 1/72

= 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/8.9

= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/8 - 1/9

= 1 - 1/9

= 8/9

3) \(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{2019}\right)\)

= \(\frac{1}{2}.\frac{2}{3}...\frac{2019}{2020}\)

= \(\frac{1.2....2019}{2.3...2020}\)

= \(\frac{1}{2020}\)

4) A = \(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{512}\)

       = \(\frac{1}{2^2}+\frac{2}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^9}\)

=> 2A = \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^8}\)

Lấy 2A - A = \(\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^8}\right)-\left(\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^9}\right)\)

             A  = \(\frac{1}{2}-\frac{1}{2^9}\)

bỏ bớt ra ik, nhìn v nhìu quá

vậy từ a - e thui vậy