B = \(\dfrac{3}{3\times5}\) + \(\dfrac{3}{5\times7}\) + \(\dfrac{3}{7\times9}\) +.....+  \(\dfrac{3}{99\times101}\)

B = \(\dfrac{3}{2}\) x ( \(\dfrac{2}{3\times5}\) + \(\dfrac{2}{5\times7}\) +\(\dfrac{2}{7\times9}\) +.....+ \(\dfrac{2}{99\times101}\))

B = \(\dfrac{3}{2}\) x ( \(\dfrac{1}{3}\)- \(\dfrac{1}{5}\)  + \(\dfrac{1}{5}\) - \(\dfrac{1}{7}\) + .......+ \(\dfrac{1}{99}\) - \(\dfrac{1}{101}\))

B = \(\dfrac{3}{2}\) x ( \(\dfrac{1}{3}\) - \(\dfrac{1}{101}\))

B = \(\dfrac{3}{2}\) x \(\dfrac{98}{3.101}\)

B = \(\dfrac{49}{101}\)

49/101

\(A=\dfrac{1}{5}+\dfrac{1}{5^2}+...+\dfrac{1}{5^{2016}}\)

\(\Leftrightarrow\dfrac{1}{5}A=\dfrac{1}{5^2}+\dfrac{1}{5^3}+...+\dfrac{1}{5^{2017}}\)

\(\Rightarrow A-\dfrac{1}{5}A=\dfrac{1}{5}-\dfrac{1}{5^{2017}}\)

\(\Leftrightarrow\dfrac{4A}{5}=\dfrac{1}{5}-\dfrac{1}{5^{2017}}\)

\(\Leftrightarrow A=\dfrac{1}{4}-\dfrac{1}{4.5^{2016}}< \dfrac{1}{4}\)

   A   =            1/5 + 1/5² +  1/5³+ ......+1/5²⁰¹⁵ + 1/5²⁰¹⁶

 5.A  =       1+ 1/5 + 1/5²  + 1/5³+.......+ 1/5²⁰¹⁵

 5A -  A =     1 -  1/5²⁰¹⁵

    4A =        1 - 1/5²⁰¹⁵

      A = ( 1 -  1/5²⁰¹⁵): 4

     A = 1/4 - 1/\(4.5^{2016}\) < 1/4 

= [(-20/3) . (-18/5)]³

= 13824

(-2)^x=8^3=2^9

=>x thuộc rỗng vì (-2)^9 là âm

Đặt `A=9^2+9^3+...+9^2021+9^2022`

`=> 9A=9^3+9^4+...+9^2022+9^2023`

`=> 9A-A=(9^3+9^4+...+9^2022+9^2023)-(9^2+9^3+...+9^2021+9^2022)`

`=> 8A=9^2023-9`

`=> A=(9^2023-9)/8`

888888888888X9999999999999

\(27^{13}\times81^{12}\)

\(=\left(3^3\right)^{13}\times\left(3^4\right)^{12}\)

\(=3^{39}\times3^{48}\)

\(=3^{39+48}\)

\(=3^{87}\)