3906/3125

=781/3125

5A=(1/5+1/25+1/125+1/625+1/3125)*5

5A=(1+1/5+1/25+1/125+1/625)

5A-A=(1+1/5+1/25+1/125+1/625)-(1/5+1/25+1/125+1/625+1/3125)=1-1/3125

4A=1-1/3125=3124/3125

A=3124/3125:4=781/3125.

lớp 4 mÀ

\(\dfrac{1}{25}\)+\(\dfrac{1}{625}\)+\(\dfrac{1}{3125}\)=\(\dfrac{125}{3125}\)+\(\dfrac{5}{3125}\)+\(\dfrac{1}{3125}\)

=\(\dfrac{131}{3125}\)

chúc bạn học tốt ạ

a) \(2^n:4=16\Rightarrow2^n:2^2=2^4\Rightarrow2^{n-2}=2^4\Rightarrow n-2=4\Rightarrow n=6\)

b) \(6\cdot2^n+3\cdot2^n=9\cdot2^9\)

=> \(\left(6+3\right)\cdot2^n=9\cdot2^9\)

=> \(9\cdot2^n=9\cdot2^9\Rightarrow n=9\)

c) \(3^n:3^2=243\)

=> \(3^{n-2}=3^5\)

=> n - 2 = 5 => n = 7

d) 25 < 5ⁿ < 3125

=> 5² < 5ⁿ < 5⁵

=> n \(\in\){3;4}

A = 3/1×5 + 3/5×9 + 1/9×13 + ... + 9/97×101 + 3/101×105

A = 3/4 × (4/1×5 + 4/5×9 + 4/9×13 + ... + 4/97×101 + 4/101×105)

A = 3/4 × (1 - 1/5 + 1/5 - 1/9 + 1/9 - 1/13 + ... + 1/97 - 1/101 + 1/101 - 1/105)

A = 3/4 × (1 - 1/105)

A = 3/4 × 104/105

A = 26/35

B = 1/5 + 1/25 + 1/125 + 1/625 + 1/3125 + 1/15625

5B = 1 + 1/5 + 1/25 + 1/125 + 1/625 + 1/3125

5B - B = (1 + 1/5 + 1/25 + 1/125 + 1/625 + 1/3125) - (1/5 + 1/25 + 1/125 + 1/625 + 1/3125 + 1/15625)

4B = 1 - 1/15625

4B = 15624/15625

B = 15624/15625 : 4

B = 3906/15625

C = 1 + 2 + 4 + 8 + 16 + ... + 2048 + 4096

2C = 2 + 4 + 8 + 16 + 32 + ... + 4096 + 8192

2C - C = (2 + 4 + 8 + 16 + 32 + ... + 4096 + 8192) - (1 + 2 + 4 + 8 + ... + 2048 + 4096)

B = 8192 - 1

B = 8191

Soyeon_Tiểu Bàng Giải lm đúng òi

A = 3/1×5 + 3/5×9 + 1/9×13 + ... + 9/97×101 + 3/101×105

A = 3/4 × (4/1×5 + 4/5×9 + 4/9×13 + ... + 4/97×101 + 4/101×105)

A = 3/4 × (1 - 1/5 + 1/5 - 1/9 + 1/9 - 1/13 + ... + 1/97 - 1/101 + 1/101 - 1/105)

A = 3/4 × (1 - 1/105)

A = 3/4 × 104/105

A = 26/35

B = 1/5 + 1/25 + 1/125 + 1/625 + 1/3125 + 1/15625

5B = 1 + 1/5 + 1/25 + 1/125 + 1/625 + 1/3125

5B - B = (1 + 1/5 + 1/25 + 1/125 + 1/625 + 1/3125) - (1/5 + 1/25 + 1/125 + 1/625 + 1/3125 + 1/15625)

4B = 1 - 1/15625

4B = 15624/15625

B = 15624/15625 : 4

B = 3906/15625

C = 1 + 2 + 4 + 8 + 16 + ... + 2048 + 4096

2C = 2 + 4 + 8 + 16 + 32 + ... + 4096 + 8192

2C - C = (2 + 4 + 8 + 16 + 32 + ... + 4096 + 8192) - (1 + 2 + 4 + 8 + ... + 2048 + 4096)

B = 8192 - 1

B = 8191

Ta có:

a)\(25< 2^x< 3125\)

\(\Rightarrow2^4< 2^x< 2^{12}\)

\(\Rightarrow4< x< 12\)

b)\(\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=7450\)

\(\Rightarrow100x+5050=7450\Rightarrow10x=2400\Rightarrow x=240\)

c)\(1+2+3+..+x=\frac{x\left(x+1\right)}{2}=78.\)

\(\Rightarrow x\left(x+1\right)=156\)\(\Rightarrow x=12\)

d)\(12x+13x=25x=2000\Rightarrow x=80\)

e)\(6x+4x=10x=2010\Rightarrow x=201\)

Bài 1:

a) \(\dfrac{10^6\times10^2}{1000^3}=\dfrac{10^{6+2}}{\left(10^3\right)^3}=\dfrac{10^8}{10^9}=\dfrac{1}{10}\)

b)\(\dfrac{625^2\times57\times3125}{25}=\dfrac{\left(5^4\right)^2\times5^5\times57}{5^2}=\dfrac{5^{13}\times57}{5^2}=5^{11}\times57\)

Bài 2 :

a) (x - 5)⁵ = (x - 5)¹⁰

⇒ x - 5 = 0 hoặc x - 5 = 1

⇒ x ∈ {5 ; 6}

a) 

5²x .5  = 3125

25x .5 = 3125

25x     = 3125 : 5

25x     = 625

x         = 625 : 25

x         = 25

a) 5^2x . 5 = 3125

5^{2x + 1} = 5⁵

\(\Rightarrow\)2x + 1 = 5

\(\Rightarrow\)2x = 5 - 1 = 4

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

b) 5^x + 5^{x + 3} = 630

5^x + 5^x . 5³ = 630

5^x . ( 1 + 5³ ) = 630

5^x . 126 = 630

5^x = 630 : 126

5^x = 5

\(\Rightarrow\)x = 5

c) 3^{2x + 1} = 243

3^{2x + 1} = 3⁵

\(\Rightarrow\)2x + 1 = 5

\(\Rightarrow\)2x = 5 - 1 = 4

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

d) 3^{2x + 1} = 9

3^{2x + 1} = 3²

\(\Rightarrow\)2x + 1 = 2

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

\(\Rightarrow\)x = 1 : 2 = \(\frac{1}{2}\)

a) 5^2x.5=3135

=> 5^2x   =3125:5

=> 5^2x   =625

=> 5^2x   = 5^4

=> 2x       =4

=>   x       =4:2

=>  x        =2

Vậy x=2

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chị chỉ gợi ý cko em cách làm được không ?