1,

ta có : \(\frac{\overline{abab}}{\overline{cdcd}}=\frac{\overline{abab}:101}{\overline{cdcd}:101}=\frac{\overline{ab}}{\overline{cd}}\) ; \(\frac{\overline{ababab}}{\overline{cdcdcd}}=\frac{\overline{ababab}:10101}{\overline{cdcdcd}:10101}=\frac{\overline{ab}}{\overline{cd}}\)

Vậy \(\frac{\overline{abab}}{\overline{cdcd}}=\frac{\overline{ababab}}{\overline{cdcdcd}}\)

2, 

\(\frac{1}{2}.\frac{1}{b}=\frac{2}{4}\)

\(\Rightarrow\frac{1.1}{2.b}=\frac{2}{4}\)

\(\Rightarrow\frac{1}{2.b}=\frac{1}{2}\)

\(\Rightarrow2.b=2\)

\(\Rightarrow b=2:2=1\)

\(\frac{abab}{cdcd}=\frac{abab:101}{cdcd:101}=\frac{ab}{cd}\)

mà \(\frac{ababab}{cdcdcd}=\frac{ababab:10101}{cdcdcd:10101}=\frac{ab}{cd}\)

=> \(\frac{abab}{cdcd}=\frac{ababab}{cdcdcd}\)

vậy...

câu 2

\(\frac{1}{2}.\frac{1}{b}=\frac{2}{4}\\ \Rightarrow\frac{1}{b}=\frac{2}{4}:\frac{1}{2}=1\\ \Rightarrow b=1\)

vậy....

a, vận dụng cái chia hết

tìm ước chung lớn nhất

chúc lm đc bài

A = 1/2^2 + 1/3^2 + 1/4^2 + ... + 1/100^2

1/2^2 < 1/1*2

1/3^2 < 1/2*3

1/4^2 < 1/3*4

...

1/100^2 < 1/99*100

=> A < 1/1*2 + 1/2*3 + 1/3*4 + ... + 1/99*100

=> A < 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/99 - 1/100

=> A < 1 - 1/100

=> A < 1

minh deo can ban k dau :((

\(a,\frac{1}{2}x+\frac{3}{5}(x-2)=3\)

\(\Rightarrow\frac{1}{2}x+\frac{3}{5}x-\frac{6}{5}=3\)

\(\Rightarrow\left[\frac{1}{2}+\frac{3}{5}\right]x=3+\frac{6}{5}\)

\(\Rightarrow\left[\frac{5}{10}+\frac{6}{10}\right]x=\frac{21}{5}\)

\(\Rightarrow\frac{11}{10}x=\frac{21}{5}\)

\(\Rightarrow x=\frac{21}{5}:\frac{11}{10}=\frac{21}{5}\cdot\frac{10}{11}=\frac{21}{1}\cdot\frac{2}{11}=\frac{42}{11}\)

Vậy x = 42/11

Mình ko bít có đúng ko nên sai đừng trách mình nhé !

\(A=\frac{7^{2011}+1}{7^{2013}+1}\)

\(7^2.A=\frac{7^{2013}+49}{7^{2013}+1}=\frac{7^{2013}+1+48}{7^{2013}+1}=\)\(\frac{7^{2013}+1}{7^{2013}+1}+\frac{48}{7^{2013}+1}=1\frac{48}{7^{2013}+1}\)

\(B=\frac{7^{2013}+1}{7^{2015}+1}\)

\(7^2.B=\)\(=\frac{7^{2015}+49}{7^{2015}+1}=\)\(\frac{7^{2015}+1+48}{7^{2015}+1}=\)\(\frac{7^{2015}+1}{7^{2015}+1}+\frac{48}{7^{2015}+1}=1\frac{48}{7^{2015}+1}\) 

 \(Vì\) \(1\frac{48}{7^{2013}+1}>1\frac{48}{7^{2013}+1}\)​​\(\Rightarrow7^2.A>7^2.B\)\(\Rightarrow A>B\)

\(Vậy\) \(A>B\)

Bài 2 nè

ta xét B trước:

\(B=\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+..\)\(.....+\frac{1}{2015}-\frac{1}{2016}\)

   =\(\left(\frac{1}{1}+\frac{1}{3}+....+\frac{1}{2015}\right)-\)\(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}....+\frac{1}{2016}\right)\)

\(=\)\(\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{2016}\right)-\)\(\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{1008}\right)\)

\(=\frac{1}{1009}+\frac{1}{1010}+....+\frac{1}{2016}\)

vậy A:B\(=\frac{1}{1009}+\frac{1}{1010}+....+\frac{1}{2016}\)\(:\frac{1}{1009}+\frac{1}{1010}+....+\frac{1}{2016}\)

\(=1\)