a)

\(A=5^{50}-5^{48}+5^{46}-5^{44}+...+5^6-5^4+5^2-1\)

\(5^2.A=5^2.\left(5^{50}-5^{48}+5^{46}-5^{44}+...+5^6-5^4+5^2-1\right)\)

\(25A=5^{52}-5^{50}+5^{48}-5^{46}+...+5^8-5^6+5^4-5^2\)

\(A+25A=\left(5^{50}-5^{48}+5^{46}-5^{44}+...+5^6-5^4+5^2-1\right)+\left(5^{52}-5^{50}+5^{48}-5^{46}+...+5^8-5^6+5^4-5^2\right)\)

\(26A=5^{22}-1\)

\(A=\dfrac{5^{22}-1}{26}\).

b)

\(26A+1=5^n\)

\(\Leftrightarrow\left(5^{52}-1\right)+1=5^n\)

\(\Leftrightarrow5^{52}=5^n\)

\(\Rightarrow n=52\).

c)

\(A=\left(5^{50}-5^{48}\right)+\left(5^{46}-5^{44}\right)+...+\left(5^6-5^4\right)+\left(5^2-1\right)\)

\(=5^{48}.\left(5^2-1\right)+5^{44}.\left(5^2-1\right)+...+5^4.\left(5^2-1\right)+1.\left(5^2-1\right)\)

\(=5^2.24.\left(5^{46}+5^{42}+...+5^2\right)+24\)

\(=25.4.6.\left(5^{46}+5^{42}+...+5^2\right)+24\)

\(=100.6.\left(5^{46}+5^{42}+...+5^2\right)+24⋮100\)

\(\Rightarrow A⋮100\).

\(A=\dfrac{-9}{10^{2010}}+\dfrac{-19}{10^{2011}}=\dfrac{-90}{10^{2011}}+\dfrac{-19}{10^{2011}}=\dfrac{-109}{10^{2011}}\)

\(B=\dfrac{-9}{10^{2011}}+\dfrac{-19}{10^{2010}}=\dfrac{-9}{10^{2011}}+\dfrac{-190}{10^{2011}}=\dfrac{-199}{10^{2011}}\)

Mà \(\dfrac{-109}{10^{2011}}>\dfrac{-199}{10^{2011}}\)

\(\Rightarrow A>B\).

tao chịu ,

chắc mày bít t là ai

`(12/999 +23/200 -34/201 ) .(1/2-1/3-1/6)`

`= (12/999 +23/200 -34/201 ) .( 3/6 - 2/6-1/6)`

` =(12/999 +23/200 -34/201 ) . 0/6`

` =(12/999 +23/200 -34/201 ) . 0`

`=0`

   ( - \(\dfrac{2}{3}\) + 1\(\dfrac{1}{4}\) - \(\dfrac{1}{6}\)) - \(\dfrac{24}{10}\)

= - \(\dfrac{2}{3}\)  + \(\dfrac{5}{4}\)  - \(\dfrac{1}{6}\) - \(\dfrac{24}{10}\)

= \(\dfrac{-40}{60}\) + \(\dfrac{25}{60}\) - \(\dfrac{10}{60}\) - \(\dfrac{144}{60}\)

= \(-\dfrac{169}{60}\)

`1/5 + 1/6 -1/10 +1/12 + 1/7 -1/14`

`= (1/5-1/10)+(1/6+1/12)+(1/7-1/14)`

`= (2/10-1/10) +(2/12+1/12) +(2/14-1/14)`

`= 1/10 + 1/4 + 1/14`

`= 4/40 + 10/40 +1/14`

`= 14/40 + 1/14`

`=7/20 +1/14`

`=59/140`

\(B=\dfrac{1}{5}+\dfrac{1}{6}-\dfrac{1}{10}+\dfrac{1}{12}+\dfrac{1}{7}-\dfrac{1}{14}\)

\(B=\left(\dfrac{1}{5}-\dfrac{1}{10}\right)+\left(\dfrac{1}{6}+\dfrac{1}{12}\right)+\left(\dfrac{1}{7}-\dfrac{1}{14}\right)\)

\(B=\left(\dfrac{2}{10}-\dfrac{1}{10}\right)+\left(\dfrac{2}{12}+\dfrac{1}{12}\right)+\left(\dfrac{2}{14}-\dfrac{1}{14}\right)\)

\(B=\dfrac{1}{10}+\dfrac{1}{4}+\dfrac{1}{14}\)

\(B=\dfrac{14}{140}+\dfrac{35}{140}+\dfrac{10}{140}\)

\(B=\dfrac{59}{140}\)

Câu `a` chỗ `3'7` là `3/7` nhỉ?

`a)5/11 . 6/11:3/7`

`=30/121 . 7/3`

`=70/121`

`b)5/2+13/4:2-17/4`

`=5/2+13/8-17/4`

`=33/8-17/4`

`=-1/8`

`a, 5/11 . 6/11 : 3/7`

`= 5/11 . 6/11 . 7/3`

`=(5.6.7)/(11.11.3)`

`= 210/363`

`=70/121`

`b, 5/2 + 13/4 : 2 -17/4`

`=  5/2 + 13/4 . 1/2-17/4`

`=5/2 +13/8-17/4`

`=20/8+13/8-17/4`

`= 33/8 -17/4`

`=33/8 - 34/8`

`=-1/8`

`8/15-x:3/4=11/18`

`x:3/4=8/15-11/18`

`x:3/4=-7/90`

`x=-7/90 . 3/4`

`x=-7/120`

\(\dfrac{8}{15}-x:\dfrac{3}{4}=\dfrac{11}{18}\)

          \(x:\dfrac{3}{4}=\dfrac{8}{15}-\dfrac{11}{18}\)   

          \(x:\dfrac{3}{4}=-\dfrac{7}{90}\)

          \(x=-\dfrac{7}{90}.\dfrac{3}{4}\)

          \(x=-\dfrac{7}{120}\)

       Vậy \(x=-\dfrac{7}{120}\)

\(\left(x-3\right)^{2x}:\left(x-3\right)^x=1\)

\(\Rightarrow\left(x-3\right)^{2^x}:\left(x-3\right)^x=1\)

\(\Rightarrow\left(x-3\right)^2:\left(x-3\right)^x=1\)

Mà kết quả ở đây bằng 1 nên chỉ có 1 phép chia duy nhất là \(1:1=1\)

Vậy \(\left(x-3\right)^2=\left(x-3\right)^x=1;\)

\(\Rightarrow\left(x-3\right)=\left(x-3\right)=1\) vì chỉ có lũy thừa của 1 mới bằng 1.

\(\Rightarrow x=3+1=4\)

cảm ơn ạ