\(A=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{99}}\)

\(\Rightarrow\dfrac{A}{3}=\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{100}}\)

\(\Rightarrow A-\dfrac{A}{3}=\dfrac{2A}{3}=\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{99}}\right)-\left(\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{100}}\right)\)

\(\Rightarrow\dfrac{2A}{3}=\left(\dfrac{1}{3^2}-\dfrac{1}{3^2}\right)+\left(\dfrac{1}{3^3}-\dfrac{1}{3^3}\right)+...+\left(\dfrac{1}{3^{99}}-\dfrac{1}{3^{99}}\right)+\left(\dfrac{1}{3}-\dfrac{1}{3^{100}}\right)=\dfrac{1}{3}-\dfrac{1}{3^{100}}\)

\(\Rightarrow2A=3\cdot\left(\dfrac{1}{3}-\dfrac{1}{3^{100}}\right)\)

\(\Rightarrow\text{A}=\dfrac{1-\dfrac{1}{3^{99}}}{2}\)

\(\Rightarrow A=\dfrac{1}{2}-\dfrac{1}{2.3^{99}}< \dfrac{1}{2}\)

Bài 2 : 1 + ( -2 ) + 3 + ( -4 )  + ... + 2015

= [ 1 + ( -2 ) ] + [ 3 + ( -4 ) ] + ... + 2015

= -1 + -1 + ... + 2015

Có số các cặp số bằng ( -1 ) là : 

2014 : 2 = 1007 ( cặp ) 

= -1007 + 2015

= 1008

Bài 1 sai đề

a,48:(7x-15)=8

7x-15=6

7x=21

x=3

b,100-3(5-x)=73

3(5-x)=27

5-x=9

x=-4

c,[(x+32)-17]*2+8=50

[(x+32)-17]*2=42

(x+32)-17=21

x+32=38

x=6

a)48:(7x-15)=8

         (7x-15)=48:8

         (7x-15)=6

                7x=6+15

                 7x=21

                   x=21:7

                   x=3

b)100-3(5-x)=73

          3(5-x)=100-73

         3(5-x)=27

            5-x=27:3

             5-x=9

                x=5-9

                x=-4

c)[(x+32)-17]x2+8=50

   [(x+32)-17]x2=50+8=58

   [(x+32)-17]=58:2

          x+32   =29+17

          x         =46-32

         x           =14

\(∘backwin\)

\(a ) ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ... + ( x + 100 ) = 5750\)

\( ( x + x + x + ... + x ) + ( 1 + 2 + 3 + ... + 100 ) = 5750 \)

\( 100 x + ( 1 + 100 ) ×100 : 2 = 5750\)

\(100 x + 5050 = 5750\)

\( 100 x = 5750 − 5050\)

\(100 x = 700\)

\(x = 700 : 100\)

\(x = 7\)

\(b,\) \(B=\)\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{2021^2}< \dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2020}+2021\)

\( B < 1 -\)\(\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2020}-\dfrac{1}{2021}\)

\(B<1-\)\(\dfrac{1}{2021}\)

\(B<\)\(\dfrac{2020}{2021}\)

\(\dfrac{2020}{2021}< 1\)

\(B<1\)

a) (x+1) +(x+2 ) + ...+(x+100)=5750
= 100x + (1+2+3+...+100) = 5750
=100x + 5050 = 5750
--> 100x = 5750-5050=700
--> x=7

b) Ta thấy: 1/2^2 < 1/2.3
                  1/3^2 < 1/3.4
                        ...
                  1/2021^2 < 1/2021.2022
--> B=1/2^2 + 1/3^2 + 1/4^2 + ...+ 1/2021^2 < 1/2.3 + 1/3.4 + ... +1/2021.2022 (1)
     Ta có: 1/2.3 + 1/3.4 + ... +1/2021.2022
         =1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2021 - 1/2022
         =1/2 - 1/2022 < 1 (2)
Từ (1) và (2) --> B<1 (đpcm)
                                                                      < 
                                                                     

c) !2-x!+2=x

!x-2!=x-2

đúng với mọi x>=2

Tập ghi có dấu đi bạn ei

ghi như thế méo ai hiểu đâu

và......kết bạn nha!

>< :3 :))

a. ( 135 - 35 ) ( -47 ) + 53 ( -48 - 52 )

= 100 ( -47 ) + 53 ( -100 )

= -4700 + -5300

= -10000

b. 25 ( 75 - 49 ) + 75 | 25 - 49 |

= 25 . 26 + 75 | -24 |

= 650 + 75 . 24

= 650 + 1800

=2450

a, 96-3(x+1)= 42

      3(x+1)  = 96-42

       3(x+1) = 54

           x+1 = 54:3

            x+1= 18

               x = 18-1

               x = 17

b, 5(x+35) = 515 

        x+35 = 515:5

        x+35 = 103

            x  = 103-35

             x = 68

c, 12x-33=3².3³

    12x-33= 3⁵

    12x-33=243

        12x=243+33

        12x= 276

           x = 276:12

          x  = 23        

 (x + 1) + (x + 2) + (x + 3 )+ ... + (x + 20) = 250 ( có 20 nhóm )
=> ( x + x + x +...+ x ) + ( 1 + 2 + 3 +...+ 20) = 250 ( có 20 x và 20 số hạng )
=> x . 20 + 20 . 21 : 2 = 250
=> x . 20 + 210 = 250
=> x . 20 = 250 - 210
=> x . 20 = 40
=> x = 40 : 20
     x = 2

(x+1)+(x+2)+(x+3)+...+(x+20)=250

Dãy trên có 20 số hạng

20x+(1+2+3+...+20)=250

Tổng dãy 1+2+3+...+20 là

(20+1).20:2=210

20x+210=250

20x=250-210

20x=40

x=40:20

x=2

(x + 1) + (x + 2) + (x + 3 )+ ... + (x + 20) = 250

250 = ( 1 + 2 + 3 + ... + 20 ) + ( 20 x x )

250 = 210 + ( 20 x X ) 

X = ( 250 - 210 ) : 20

X = 2. k mình nha