\(A=\frac17+\frac{1}{7^2}+\frac{1}{7^3}+\frac{1}{7^4}+\ldots+\frac{1}{7^{2024}}+\frac{1}{7^{2025...">
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11 tháng 11 2025

Ta có: \(A=\frac17+\frac{1}{7^2}+\cdots+\frac{1}{7^{2025}}\)

=>\(7A=1+\frac17+\cdots+\frac{1}{7^{2024}}\)

=>\(7A-A=1+\frac17+\cdots+\frac{1}{7^{2024}}-\frac17-\frac{1}{7^2}-\cdots-\frac{1}{7^{2025}}\)

=>\(6A=1-\frac{1}{7^{2025}}\)

=>\(1-\frac{1}{7^{x}}=1-\frac{1}{7^{2025}}\)

=>\(7^{x}=7^{2025}\)

=>x=2025

2 tháng 8 2016

a ) \(1\frac{1}{2}+x=\frac{3}{7}-7\)

\(\frac{3}{2}+x=-\frac{46}{7}\)

\(x=-\frac{46}{7}-\frac{3}{2}\)

\(x=-\frac{113}{14}\)

9 tháng 7 2019

\(A=\frac{99}{100}-\left(\frac{1}{1.2}+\frac{1}{2.3}+..+\frac{1}{99.100}\right)\)

\(A=\frac{99}{100}-\left(1-\frac{1}{100}\right)\)

\(A=\frac{99}{100}-\frac{99}{100}\)

\(A=\frac{99-99}{100}=0\)

Bài 2 

\(\left(3x+5\right).\left(2x-4\right)=0\)

\(TH1:3x+5=0\)

\(3x=-5\)

\(x=-\frac{5}{3}\)

\(TH2:2x-4=0\)

\(2x=4\)

\(x=2\)

\(\left(x^2-1\right).\left(x+3\right)=0\)

\(\Rightarrow x^2-1=0\)

\(x^2=1\)

\(\Rightarrow x=1\)

\(x+3=0\)

\(x=-3\)

\(5x^2-\frac{1}{2}x=0\)

\(\Rightarrow5x^2-\frac{x}{2}=0\)

\(\Rightarrow5x^2=\frac{5x^2}{1}=\frac{5x^2.2}{2}\)

\(10x^2-x=x.\left(10x-1\right)\)

\(\frac{x.\left(10x-1\right)}{2}=0\)

\(\frac{x.\left(10x-1\right)}{2}.2=0.2\)

\(10x-1=0\)

\(x=\frac{1}{10}=0.100\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{1}{10}=0.100\\x=0\end{cases}}\)

\(\frac{x}{4}-\frac{1}{2}=\frac{3}{4}\)

\(\frac{x}{4}=\frac{3}{4}+\frac{1}{2}\)

\(\frac{x}{4}=\frac{5}{4}\)

\(\Rightarrow x=5\)

\(\frac{1}{8}+\frac{7}{8}:x=\frac{3}{4}\)

\(\frac{7}{8}:x=\frac{3}{4}-\frac{1}{8}\)

\(x=\frac{7}{8}:\frac{5}{8}\)

\(x=\frac{56}{40}=\frac{28}{20}=\frac{14}{10}=\frac{7}{5}\)

7 tháng 8 2018

Bài 1:

a)  \(x-\frac{20}{11.13}-\frac{20}{13.15}-...-\frac{20}{53.55}=\frac{3}{11}\)

\(x-\left(\frac{20}{11.13}+\frac{20}{13.15}+...+\frac{20}{53.55}\right)=\frac{3}{11}\)

\(x-\frac{20}{2}.\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)

\(x-10.\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)

\(x-10\cdot\frac{4}{55}=\frac{3}{11}\)

\(x-\frac{8}{11}=\frac{3}{11}\)

\(x=1\)

b) \(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\)

\(\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\)

\(\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\)

\(2.\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2}{9}\)

\(2.\left(\frac{1}{6}-\frac{1}{x+1}\right)=\frac{2}{9}\)

\(\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)

\(\frac{1}{x+1}=\frac{1}{18}\)

=> x + 1 =18

x = 17

bài 2 ko bk lm, xl nha

7 tháng 8 2018

mk cảm ơn bn nha

31 tháng 12 2016

Bài 1:
\(\frac{\frac{5}{131}+\frac{5}{141}-\frac{5}{191}-\frac{5}{4011}}{\frac{7}{131}+\frac{7}{141}+\frac{7}{-191}-\frac{7}{4011}}=\frac{5\left(\frac{1}{131}+\frac{1}{141}-\frac{1}{191}-\frac{1}{4011}\right)}{7\left(\frac{1}{131}+\frac{1}{141}-\frac{1}{191}-\frac{1}{4011}\right)}=\frac{5}{7}\)

Bài 2:
a) \(\frac{x}{7}+\left(\frac{-3}{7}\right)^2=\frac{2}{7}:\frac{4}{3}\)

\(\Rightarrow\frac{x}{7}+\frac{9}{49}=\frac{3}{14}\)

\(\Rightarrow\frac{x}{7}=\frac{3}{98}\)

\(\Rightarrow98x=21\)

\(\Rightarrow x=\frac{3}{14}\)

Vậy \(x=\frac{3}{14}\)

b) \(\left(x-1\right)^{x+6}=\left(x-1\right)^{x+4}\)

\(\Rightarrow\left(x-1\right)^{x+6}-\left(x-1\right)^{x+4}=0\)

\(\Rightarrow\left(x-1\right)^{x+4}.\left[\left(x-1\right)^2-1\right]=0\)

\(\Rightarrow\left(x-1\right)^{x+1}=0\) hoặc \(\left(x-1\right)^2-1=0\)

+) \(\left(x-1\right)^{x+1}=0\Rightarrow x-1=0\Rightarrow x=1\)

+) \(\left(x-1\right)^2-1=0\)

\(\Rightarrow\left(x-1\right)^2=1\)

\(\Rightarrow\left(x-1\right)=\pm1\)

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

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

Vậy \(x\in\left\{0;2;1\right\}\)

31 tháng 12 2016

1)

\(\frac{\frac{5}{131}+\frac{5}{141}-\frac{5}{191}-\frac{5}{4011}}{\frac{7}{131}+\frac{7}{141}+\frac{7}{-191}-\frac{7}{4011}}\)

\(=\frac{5\left(\frac{1}{131}+\frac{1}{141}-\frac{1}{191}-\frac{1}{4011}\right)}{7\left(\frac{1}{131}+\frac{1}{141}-\frac{1}{191}-\frac{1}{4011}\right)}\)

\(=\frac{5}{7}\)

2) \(\frac{x}{7}+\left(-\frac{3}{7}\right)^2=\frac{2}{7}:\frac{4}{3}\)

\(=\frac{x}{7}+\frac{9}{49}=\frac{3}{14}\)

\(=\frac{x}{7}=\frac{3}{14}-\frac{9}{49}=\frac{3}{98}\)

\(\Rightarrow98x=21\)

\(\Rightarrow x=\frac{3}{14}\)

7 tháng 8 2018

\(\frac{x+2}{x+6}=\frac{3}{x+1}\)

\(\Rightarrow\left(x+2\right)\left(x+1\right)=3\left(x+6\right)\)

\(\Rightarrow x^2+x+2x+2=3x+18\)

\(\Rightarrow x^2+x+2x-3x=18-2\)

\(\Rightarrow x^2=16\)

\(\Rightarrow x=\pm4\)

các phần còn lại tương tự :)

7 tháng 8 2018

a)\(\frac{x+2}{x+6}\) =\(\frac{3}{x+1}\)

<=>\(\frac{\left(x+2\right)\left(x+1\right)}{\left(x+6\right)\left(x+1\right)}\) =\(\frac{3\left(x+6\right)}{\left(x+1\right)\left(x+6\right)}\)

=> ( x+2) ( x+1) = 3(x+6)

<=>  x2 +3x +3 = 3x +18

<=> x2 +3x -3x = 18 -3 

<=> x2              = 15

 => x                 = \(\sqrt{15}\)

 Vậy x=\(\sqrt{15}\)

b)