Question

[rinjin]

Tính

a)\((\dfrac{3}{4}-81).(\dfrac{3^2}{5}-81).(\dfrac{3^3}{6}-81)...(\dfrac{3^{2000}}{2003}-81)\)
b)\(\dfrac{69}{157}-(2+(3+(4+5^{-1})^{-1})^{-1}\)

Answer 1

[Nguyễn Lê Phước Thịnh]

a: \(\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)

\(=\left(\dfrac{3^6}{9}-81\right)\left(\dfrac{3}{4}-81\right)\cdot\left(\dfrac{3^2}{5}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)

\(=\left(81-81\right)\left(\dfrac{3}{4}-81\right)\cdot\left(\dfrac{3^2}{5}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)

=0

b: \(\dfrac{69}{157}-\left(2+\left(3+4+5^{-1}\right)^{-1}\right)^{-1}\)

\(=\dfrac{69}{157}-\left(2+\left(3+4+\dfrac{1}{5}\right)^{-1}\right)^{-1}\)

\(=\dfrac{69}{157}-\left(2+1:\dfrac{36}{5}\right)^{-1}\)

\(=\dfrac{69}{157}-\left(2+\dfrac{5}{36}\right)^{-1}\)

\(=\dfrac{69}{157}-\left(\dfrac{77}{36}\right)^{-1}\)

\(=\dfrac{69}{157}-\dfrac{36}{77}=\dfrac{-339}{12089}\)