a: =>1/3*4+1/4*5+...+1/x(x+1)=10/39

=>1/3-1/4+...+1/x-1/x+1=10/39

=>1/3-1/(x+1)=10/39

=>1/(x+1)=13/39-10/39=3/39=1/13

=>x+1=13

=>x=12

b: =>15x=150

=>x=10

c: =>120-5x=45

=>5x=75

=>x=15

`@` `\text {Ans}`

`\downarrow`

\(\left(1-\dfrac{1}{2}\right)\times\left(1-\dfrac{1}{3}\right)\times\left(1-\dfrac{1}{4}\right)\times\left(1-\dfrac{1}{5}\right)...\left(1-\dfrac{1}{1000}\right)\)

`=`\(\left(\dfrac{2}{2}-\dfrac{1}{2}\right)\times\left(\dfrac{3}{3}-\dfrac{1}{3}\right)\times\left(\dfrac{4}{4}-\dfrac{1}{4}\right)...\left(\dfrac{1000}{1000}-\dfrac{1}{1000}\right)\)

`=`\(\dfrac{1}{2}\times\dfrac{2}{3}\times\dfrac{3}{4}\times...\times\dfrac{999}{1000}\)

`=`\(\dfrac{1}{1000}\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.\dfrac{4}{5}.......\dfrac{99}{100}=\dfrac{1}{100}\)

phần 100 mà sao lại 1000,các bạn cố gắng giúp mình với nhé,mình cần gấp !

    3/2.(x-5/3)+4/5=x+1

3/2.x-3/2.5/3+4/5=x+1

          3/2.x-5/2-x=1+4/5

          3/2.x-5/2-x=9/5

                3/2.x-x=9/5+5/2

                   1/2.x=43/10

                         x=43/10:1/2

                         x=43/5

bài này cần có đkxđ 

Lời giải:

$x^2+x+1\vdots x+1$
$\Rightarrow x(x+1)+1\vdots x+1$

$\Rightarrow 1\vdots x+1$

$\Rightarrow x+1\in \left\{1; -1\right\}$

$\Rightarrow x\in \left\{0; -2\right\}$

1) 18 . x+x+x=48x25

=18 .x + 2. x=4 . 5. 12 .5

=20.x=20.60

=>x=120:20=60

2) [(2.x-5):(15+10)].20=100

(2x-5):25=20.100

(2x-5):25=2000

2x-5=2000x25

2x-5=50000

2x=50005

x=\(\frac{50005}{2}\)

1) 18.x+x+x=48.25

=> 20x=1200

=> x=60

2) [(2x-5):(15+10)].20=100

=> (2x-5):25 =5

=>2x-5= 125

=>2x=130

=>x=65

|x-1|=1

=>x-1 =1  hoặc x-1=-1

TH1: x-1=1    TH2: x-1=-1

=>x=2            =>x=0

vậy x=2,x=0

   \(|x-1|=1\)

\(\Rightarrow x-1=1\)

và  \(x-1=-1\)

Nếu \(x-1=1\)thì:

                 \(x=1+1\)  

                 \(x=2\) 

Nếu \(x-1=-1\)thì:

                 \(x=-1+1\)

                \(x=0\)

Vậy \(x\in\hept{\begin{cases}2\\0\end{cases}}\)

\(\left|x-1\right|=1\)

\(\Rightarrow\hept{\begin{cases}x-1=1\\x-1=-1\end{cases}}\)

\(\Rightarrow x\in\left\{2;0\right\}\)

( 1 + x ) + ( 2 + x ) + ( 3 + x ) + ...+ ( 100 + x ) = 2018

\(\Rightarrow\)( 1 + 2 + 3 + ... + 100 ) + ( x + x + x + ... + x ) = 2018

\(\Rightarrow\){( 1 + 100 ) . [( 100 - 1 ) : 1 + 1 ] : 2 } + ( x + x + ... + x ) = 2018

\(\Rightarrow\)5050 + x . 100 = 2018

\(\Rightarrow\)  x100 = 2018 - 5050 = -3032

\(\Rightarrow\)x = -3032 : 100 = -30,32

vậy x = -30,32

mà nè sai thì xin lỗi đề hơi có vấn đề nếu sai thì sorry nha !!!

Ta có ; \(1\dfrac{1}{10}.1\dfrac{1}{11}.....1\dfrac{1}{2011}.1\dfrac{1}{2012}\)

\(=\dfrac{11}{10}.\dfrac{12}{11}.....\dfrac{2012}{2011}.\dfrac{2013}{2012}\)
 

\(=\dfrac{2013}{10}=201,3\)

1 \(\dfrac{1}{10}\)x 1\(\dfrac{1}{11}\)x 1\(\dfrac{1}{12}\) x...x 1\(\dfrac{1}{2011}\)x 1\(\dfrac{1}{2012}\)

=\(\dfrac{11}{10}\)x \(\dfrac{12}{11}\)x \(\dfrac{13}{12}\)x \(\dfrac{2012}{2011}\)x \(\dfrac{2013}{2012}\)