A= 1 + 5 + 5² + 5 ³ + ... + 5⁸⁰⁰ 

5A=       5 + 5²  + 5³ + .... +5 ⁸⁰⁰ + 5⁸⁰¹  

5A - A = 5⁸⁰¹  - 1 

4a = 5⁸⁰¹ - 1 

    5⁸⁰¹ - 1 +1 = 5ⁿ

⇒  5⁸⁰¹ = 5ⁿ ⇒ n = 801

   \(\dfrac{4}{9}\) : \(\left(-\dfrac{1}{7}\right)\) + \(6\dfrac{5}{9}\) + \(6\dfrac{5}{19}\) : \(\left(-\dfrac{1}{7}\right)\)

= \(\dfrac{4}{9}\) . \(\left(-\dfrac{7}{1}\right)\) + \(\dfrac{59}{9}\) + \(\dfrac{119}{19}\) . \(\left(-\dfrac{7}{1}\right)\)

= \(\dfrac{-28}{9}\) + \(\dfrac{59}{9}\) + \(\dfrac{-833}{19}\)

= \(\dfrac{31}{9}\) + \(\dfrac{-833}{19}\)

= \(\dfrac{589}{171}\) + \(\dfrac{-7497}{171}\)

= \(\dfrac{-6908}{171}\)

nhanh

Em nên dùng công thức toán học để mọi người hiểu đề cho đúng

em ko bt cách ghi mũ kiểu gì ạ

???

cạn lời 

\(4^x:2^6=2^8\)

\(\Rightarrow\left(2^2\right)^x:2^6=2^8\)

\(\Rightarrow2^{2x}:2^6=2^8\)

\(\Rightarrow2^{2x-6}=2^8\)

\(\Rightarrow2x-6=8\)

\(\Rightarrow2x=14\)

\(\Rightarrow x=\dfrac{14}{2}\)

\(\Rightarrow x=7\)

$4^x:2^6=2^8$

$\Rightarrow {\left(2^2\right)}^x:2^6=2^8$

$\Rightarrow 2^{2x}:2^6=2^8$

$\Rightarrow 2^{2x-6}=2^8$

$\Rightarrow 2x-6=8$

$\Rightarrow 2x=14$

$\Rightarrow x=\genfrac{}{}{0ex}{}{14}{2}$

$\Rightarrow x=7$

Bạn nên viết lại đề bài bằng công thức toán để được hỗ trợ tốt hơn.

a) A = 2004 . 2004 = 2004² > 2002² = 2002 x 2002 = B

Vậy A > B

b) C = 143 . 143 = 143²

D = 140 . 146 + 140

D = (143 - 3)(143 + 3) + 140

D = 143² - 9 + 140 = 143² + 131 > 143² = C

Vậy C < D 

c) E = 27 . 58 = 26 . 58 + 58 > 27 + 58 . 26 = F

Vậy E > F 

\(\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{99}+\dfrac{1}{143}+\dfrac{1}{195}\\ =\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}+\dfrac{1}{195}-\dfrac{1}{63}\\ =\dfrac{1}{2}\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+\dfrac{2}{11.13}+\dfrac{2}{13.15}\right)-\dfrac{1}{63}\\ =\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{15}\right)-\dfrac{1}{63}\\ =\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{15}\right)-\dfrac{1}{63}=\dfrac{1}{2}.\dfrac{4}{15}-\dfrac{1}{63}=\dfrac{2}{15}-\dfrac{1}{63}=\dfrac{37}{315}\)

\(0,25\cdot1\dfrac{3}{5}\cdot\left(\dfrac{5}{4}\right)^2:-\dfrac{4}{7}\)

\(=\dfrac{1}{4}\cdot\dfrac{8}{5}\cdot\dfrac{25}{16}\cdot-\dfrac{7}{4}\)

\(=\dfrac{8\cdot25\cdot-7}{4\cdot5\cdot16\cdot4}\)

\(=\dfrac{1\cdot5\cdot-7}{4\cdot1\cdot2\cdot4}\)

\(=-\dfrac{35}{32}\)

nhanh

nhanh

\(\left(4-\dfrac{5}{12}\right):\left(2+\dfrac{5}{24}\right)\)

\(=\dfrac{43}{12}:\dfrac{53}{24}\)

\(=\dfrac{43}{12}\cdot\dfrac{24}{53}\)

\(=\dfrac{43\cdot2}{1\cdot53}\)

\(=\dfrac{86}{53}\)