=0:{2+4+6+...98}=0

=[1+3+5+7+...97+99]x[45x3-45x3]

=[----------------------------]x0=0

Dấu gạch trên là gì đấy?

a, [ 0 x 1 x 2 x 3 ...x 99 x 100] : [2 + 4 + 6 + ... 98]

Vì có chữ số 0 mà 0 nhân số nào cũng bằng 0 

=> 0 : ( 2 + 4 + 6 + ... 98 )

Vì số nào chia 0 cũng bằng 0 

=> 0 : ( 2 + 4 + 6 +.. + 98 ) = 0

b, Đặt A = 1 + 3 + 5 + 7 + ... + 97 + 99 )

    Đặt B = 45x 3 - 45 x 2 - 45

B = 45 x 3 - 45 x 2 - 45

B = 45 x 3 - 45 x 2 - 45 x 1

B = 45 x ( 3 - 2 - 1 )

B = 45 x 0

B = 0

Vì 0 nhân số nào cũng = 0 

=> ( 1 + 3 + 5 + 7 + ... + 97 +99 ) x 0 = 0

c, Bạn chỉ cần biến đổi tử số hoặc mẫu số giống nhau thì kết quả sẽ = 1 nha

( 0 x 1 x 2 x 3 x .... x 99 x 100 ) : ( 2 + 4 + 6 + ... + 98 )

= 0 : ( 2 + 4 + 6 + ... + 98 )

= 0

Dat S la tong phai tim. Ta có:

Sx3=1x2x3+2x3x3+3x4x3+....+99x100x3

     =1x2x(3-0)+2x3x(4-1)+3x4x(5-2)+....+99x100x(101-98)

     =(1x2x3-0x1x2)+(2x3x4-1x2x3)+(3x4x5-2x3x4)+........+99x100x101-98x99x100

     =99x100x101-0x1x2=99x100x101=999900

mik nham nhe bai 2

c, (x+1)+(x+2)+...+(x+100)=5750

\(∘backwin\)

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

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

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

\(100 x + 5050 = 5750\)

\( 100 x = 5750 − 5050\)

\(100 x = 700\)

\(x = 700 : 100\)

\(x = 7\)

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

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

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

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

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

\(B<1\)

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)
                                                                      < 
                                                                     

[1 x 2 x 3 x 4 x........................x100] x [679+679 x 123-679 x124]

  =            A                            x          [679 x 124-679 x 124]

  =            A                           x                  0

  =0         

Ban Do Thi Ngoc Trinh tra loi nhanh nhat nen minh tick!

A.   \(\left(x+1\right)+\left(x+2\right)+......+\left(x+100\right)=5750\)

      \(x+1+x+2+....+x+100=5750\)

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

      \(100x+5050=5750\)

\(100x=700\)

\(x=700:100=7\)

B.   x+(1+2+......+100) = 2000

       x + 5050 = 2000

            x = 2000 - 5050

           x= -3050

C.   ( x-1 )+(x-2)+......+( x - 100 ) = 50

 x-1+x-2+.........+x-100 = 50

100x + ( -1-2-........-100  ) = 50

100x + ( - 5050 ) = 50

100x = 50 + 5050

100 x = 5100

x = 5100 : 100

x = 51

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

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

\(100x+5050=5750\)

\(100x=5750-5050\)

\(100x=700\)

\(\Rightarrow x=\frac{700}{100}=7\)

B. \(x+\left(1+2+3+4+5+....+100\right)=2000\)

 \(x+\frac{\left(100+1\right).100}{2}=2000\)

\(x+5050=2000\)

\(\Rightarrow x=2000-5050=-3050\)

C. \(\left(x-1\right)+\left(x-2\right)+\left(x-3\right)+....+\left(x-100\right)=50\)

\(\left(x+x+x+...+x\right)-\left(1+2+3+...+100\right)=50\)

\(100x-5050=50\)

\(100x=5100\)

\(\Rightarrow x=\frac{5100}{100}=51\)