Question

a,\(\frac{x-1}{2}=\frac{x+1}{3}\)

b, \(cmr:A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99+100}nhỏhơn1\)

MỌI NGƯỜI VÀ CÔ GIÁO HÃY GIẢNG GIẢI GIÚP EM

 

 

Answer 1

Ta có : \(\frac{x-1}{2}=\frac{x+1}{3}\)

<=> \(3\left(x-1\right)=2\left(x+1\right)\)

<=> \(3x-3=2x+2\)

<=> \(3x-2x=2+3\)

<=> x = 5 

Answer 2

a, \(\frac{x-1}{2}=\frac{x+1}{3}\)

=> (x-1)3 = 2(x+1)

=> 3x - 3 = 2x + 2

=> 3x - 2x = 2 + 3

=> x = 5

b, \(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)

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

\(A=1-\frac{1}{100}=\frac{99}{100}< 1\) (ĐPCM)

Answer 3

a, 3.(x - 1) =2. ( x+ 1) 

<=>3.x-3.1=2.x+2.1

<=>3x-2x=2+3

<=>x=5

b, A= 1/1.2+1/2.3+1/3.4+...+1/99.100

=1-1/2+1/2-1/3+1/3-...+1/99-1/100

=1-1/100

=99/100

+ Vì 99/100<1 nên =>1/1.2=1/2.3+1/3.4+...+1/99.100

                 Vậy......

Answer 4

a. x-1/2 = x+1/3

=>(x-1)3=2(x+1)

=> 3x-3=2x+2

=> 3x-2x=2+3

=> x = 5

b. A = 1/1.2+1/2.3+..+1/99.100

= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ..+ 1/99 - 1/100

= 1 - 1/100 = 99/ 100 < 1