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\(\frac{3}{4}+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.........+\frac{1}{99.100}\)

\(=\frac{3}{4}+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+......+\frac{1}{99}-\frac{1}{100}\)

\(=\frac{3}{4}+1-\frac{1}{100}=\frac{87}{50}\)

giải giúp mình với ạ

Ta xét ( 4n + 2 ; 6n + 1 ) = ( 6n + 1 - ( 4n + 2 ) ; 4n + 2 ) 

= ( 2n - 1; 4n + 2 ) = ( 4n + 2 - ( 2n - 1 ); 2n - 1 ) 

= ( 2n + 1 ; 2n - 1) 

= ( 2n + 1; 2n + 1 - ( 2n - 1) ) 

= ( 2n + 1; 2 ) 

= 1

=> 4n + 2 và 6n + 1 là hai số nguyên tố cùng nhau 

=> 4n+2/6n+1 là phân số tối giản.

a, 60%x + 2/3x =1/3.6 1/3

3/5x +2/3x =1/3.19/3

x.(3/5+2/3)=19/9

x.(9/15+10/15)=19/9

x.19/15=19/9

x=19/9:19/15

x=15/9 

Vậy x=15/9

b,3.(3x-1/2)^3 +1/9=0

3.(3x-1/2)^3= -1/9

(3x-1/2)^3= -1/9:3

(3x-1/2)^3= -1/27

(3x-1/2)^3=(-1/3)^3

3x-1/2= -1/3

3x= -1/3-1/2

3x= -2/6+(-3/6)

3x= -5/6

x= -5/6 :3

x=-5/18 

Vậy x=-5/18

-5.(x+1/5) -1/2.(x-2/3)=3/2x-5/6

-5x + (-1) -1/2x -1/3=3/2x-5/6

-5x-1/2x-3/2x=1+1/3-5/6

x.(-5-1/2-3/2)= 6/6+2/6+(-5/6)

x.(-10/2+(-1/2)+(-3/2))=3/6

x.6/2=1/2

x=1/2:6/2

x=1/6

Vậy x = 1/6

3.(x-1/2) -5(x+3/5)=-x+1/5

3x - 3/2 -5x +3 = -x+1/5 

3x-5x+x= 3/2-3+1/5

x.(3-5+1)=15/10 + (-30/10)+2/10

x.(-1)= -13/10

x = -13/10 : (-1)

x=13/10

vậy x=13/10

(1-1/3)x(1-1/5)x(1-1/7)x(1-1/9)x(1-1/2)x(1-1/4)x(1-1/6)x(1-1/8)x(1-1/10)

=2/3x4/5x6/7x8/9x1/2x3/4x5/6x7/8x9/10

=2x4x6x8x1x3x5x7x9 /3x5x7x9x2x4x6x8x10

=1/10

\(b,\left(\frac{1}{2}+1\right)\left(\frac{1}{3}+1\right)\left(\frac{1}{4}+1\right)...\left(\frac{1}{99}+1\right)\)

\(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot...\cdot\frac{100}{99}\)

\(=\frac{100}{2}\)

\(=50\)

A = 1.2.3 + 2.3.4 + 3.4.5 ... + n(n + 1)(n + 2)

4A = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + ... + n(n + 1)(n + 2).4

4A = 1.2.3.4 + 2.3.4(5 - 1) + 3.4.5.(6 - 2)+ ... + n(n + 1)(n + 2)[(n + 3) - (n - 1)]

4A = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + ... + n(n + 1)(n + 2)(n + 3) - (n-1)n(n+1)(n+2)

4A = n(n+1)(n+2)(n+3)

A = n(n + 1)(n+2)(n + 3) : 4