Ta có A = \(\left(1-\frac{1}{3}\right).\left(1-\frac{1}{6}\right).\left(1-\frac{1}{10}\right)...\left(1-\frac{1}{780}\right)\)

= \(\frac{2}{3}.\frac{5}{6}.\frac{9}{10}...\frac{779}{780}=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}...\frac{1558}{1560}=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}...\frac{38.41}{39.40}=\frac{\left(1.2.3...38\right).\left(4.5.6...41\right)}{\left(2.3.4...39\right).\left(3.4.5...40\right)}\)

= \(\frac{1.41}{39.3}=\frac{41}{117}\)

rhsdhtdjdr dryh ry mnse xnyh

g

\(\left(1-\frac{1}{3}\right).\left(1-\frac{1}{6}\right).\left(1-\frac{1}{10}\right).\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{780}\right).a=1\)

=> \(\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}...\frac{779}{780}.a=1\)

=> \(\frac{4}{6}.\frac{10}{12}.\frac{18}{20}.\frac{28}{30}...\frac{1558}{1560}.a=1\)

=> \(\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}.\frac{4.7}{5.6}...\frac{38.41}{39.40}.a=1\)

=> \(\frac{1.2.3.4...38}{2.3.4.5...39}.\frac{4.5.6.7...41}{3.4.5.6...40}.a=1\)

=> \(\frac{1}{39}.\frac{41}{3}.a=1\)

=> \(\frac{41}{117}.a=1\)

=> \(a=1:\frac{41}{117}=\frac{117}{41}\)

117/41

4949/19800

a) ( 3x - 4 ) . ( x - 1 ) ³ = 0

\(\Rightarrow\orbr{\begin{cases}3x-4=0\\\left(x-1\right)^3=0\end{cases}}\Rightarrow\orbr{\begin{cases}3x=4\\x-1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{4}{3}\\x=1\end{cases}}\)

b) x¹⁷ = x

\(\Rightarrow\)x¹⁷ - x = 0

\(\Rightarrow\)x . ( x¹⁶ - 1 ) = 0

\(\Rightarrow\orbr{\begin{cases}x=0\\x^{16}-1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x^{16}=1\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)

c) 2^{2x - 1} : 4 = 8³

2^{2x - 1} : 2² = 2⁹

2^{2x - 1} = 2⁹ . 2²

2^{2x - 1} = 2¹¹

\(\Rightarrow\)2x - 1 = 11

\(\Rightarrow\)2x = 12

\(\Rightarrow\)x = 6

d) ( x + 2 ) ⁵ = 2¹⁰

( x + 2 ) ⁵ = 4⁵

\(\Rightarrow\)x + 2 = 4

\(\Rightarrow\)x = 4 - 2 = 2

e)    ( x - 5 ) ⁴ = ( x - 5 ) ⁶

( x - 5 ) ⁴ - ( x - 5 ) ⁶ = 0

( x - 5 ) ⁴ . [ 1 - ( x - 5 ) ² ] = 0

\(\Rightarrow\orbr{\begin{cases}\left(x-5\right)^4=0\\1-\left(x-5\right)^2=0\end{cases}}\Rightarrow\orbr{\begin{cases}x-5=0\\\left(x-5\right)^2=1\end{cases}}\Rightarrow\orbr{\begin{cases}x=5\\x-5=1\end{cases}}\Rightarrow\orbr{\begin{cases}x=5\\x=6\end{cases}}\)

f )  số số hạng của dãy trên là :

( x - 1 ) : 1 + 1 = x ( số )

tổng của dãy trên là :

( x + 1 ) . x : 2 = 78

( x + 1 ) . x = 78 . 2 = 156

Phân tích : 156 = 2² . 3 . 13 = ( 2² . 3 ) . 13 = 12 . 13

\(\Rightarrow\)x = 12

g)  ( x + 1 ) ² = ( x + 1 ) ⁰

( x + 1 ) ² = 1

\(\Rightarrow\)x + 1 = 1

\(\Rightarrow\)x = 1 - 1 = 0

h)  ( 2 + x ) + ( 4 + x ) + ( 6 + x ) + ... + ( 52 + x ) = 780

( 2 + 4 + 6 + ... + 52 ) + ( x + x + x + ... + x ) = 780

2 . ( 1 + 2 + 3 + ... + 26 ) + 26x = 780

2 . 351 + 26x = 780

702 + 26x = 780

26x = 780 - 702

26x = 78

x = 78 : 26

x = 3

a) (3x - 4) . (x - 1)³ = 0

+) (3x - 4) =0                                                   

3x         =0+4

3x         =4

 x          =3:4

 x          =0,75

a) (3x-4)(x-1)³=0

nen hoac 3x-4=0 hoac (x-1)³=0

                3x = 4           x-1=0

                 x=4/3            x=1

Vay x thuoc {4/3;1}

b)  x¹⁷=x 

nen x thuoc {-1;0;1}

c) 2^2x-1:4=8³

    2^2x-1  = 2⁹.2²

     2^2x-1 = 2¹¹

   => 2x-1 = 11

           2x = 12

             x=6

Vay x=6

d) (x+2)⁵=2¹⁰

   (x+2)⁵ = 4⁵

   => x+2 = 4

          x=2

Vay x= 2

e) (x-5)⁴=(x-5)⁶

x-5 thuoc {-1;0;1}

x thuoc {4;5;6}

Vay x thuoc {4;5;6}

f) \(\frac{\left(x+1\right)x}{2}=78\)

   (x+1)x=78.2

 (x+1)x=156

ma 156 = 12.13

nen x+1=13

     x=12

Vay x=12

g) (x+1)²=(x+1)⁰

x+1 thuoc {-1;0;1}

x thuoc{ -2;-1;0}

h) (2+x)+(4+x)+...+(52+x)=780

=> (2+4+...+52)+(x+x+...+x)=780

=> 702+26x=780

           26x = 78

               x=3

Vay x=3