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13 tháng 8
\(P=\left(\frac34-81\right)\left(\frac{3^2}{5}-81\right)\cdot\ldots\cdot\left(\frac{3^{15}}{18}-81\right)\)
\(P=\left(\frac34-81\right)\left(\frac{3^2}{5}-81\right)\cdot\ldots\cdot\left(\frac{3^6}{9}-81\right)\cdot\ldots\cdot\left(\frac{3^{15}}{18}-81\right)\)
\(P=\left(\frac34-81\right)\left(\frac{3^2}{4}-81\right)\cdot\ldots\cdot0\cdot\ldots\cdot\left(\frac{3^{15}}{18}-81\right)\)
\(P=0\)
TP
13 tháng 8
P=(43−81)(532−81)⋅…⋅(18315−81)
\(P = \left(\right. \frac{3}{4} - 81 \left.\right) \left(\right. \frac{3^{2}}{5} - 81 \left.\right) \cdot \ldots \cdot \left(\right. \frac{3^{6}}{9} - 81 \left.\right) \cdot \ldots \cdot \left(\right. \frac{3^{15}}{18} - 81 \left.\right)\)
\(P = \left(\right. \frac{3}{4} - 81 \left.\right) \left(\right. \frac{3^{2}}{4} - 81 \left.\right) \cdot \ldots \cdot 0 \cdot \ldots \cdot \left(\right. \frac{3^{15}}{18} - 81 \left.\right)\)
\(P = 0\)
17 tháng 12 2023
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: \(\dfrac{69}{157}-\left(2+\left(3+4+5^{-1}\right)^{-1}\right)^{-1}\)
\(=\dfrac{69}{157}-\left(2+\left(3+4+\dfrac{1}{5}\right)^{-1}\right)^{-1}\)
\(=\dfrac{69}{157}-\left(2+1:\dfrac{36}{5}\right)^{-1}\)
\(=\dfrac{69}{157}-\left(2+\dfrac{5}{36}\right)^{-1}\)
\(=\dfrac{69}{157}-\left(\dfrac{77}{36}\right)^{-1}\)
\(=\dfrac{69}{157}-\dfrac{36}{77}=\dfrac{-339}{12089}\)
8 tháng 12 2023
Đặt \(A=\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)\left(\dfrac{3^3}{6}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)
\(=\left(\dfrac{3^6}{9}-81\right)\cdot\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)
\(=\left(81-81\right)\cdot\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)
=0
31 tháng 1 2017
\(\left(\frac{3}{4}-81\right)\left(\frac{3^2}{5}-81\right)\left(\frac{3^3}{6}-81\right)....\left(\frac{3^{2000}}{2003}-81\right)\)
\(=\left(\frac{3}{4}-81\right)\left(\frac{3^2}{5}-81\right)\left(\frac{3^3}{6}-81\right)...\left(\frac{3^6}{9}-81\right)...\left(\frac{3^{2000}}{2003}-81\right)\)
\(=\left(\frac{3}{4}-81\right)\left(\frac{3^2}{5}-81\right)\left(\frac{3^3}{6}-81\right)....\left(81-81\right)...\left(\frac{3^{2000}}{2003}-81\right)\)
\(=\left(\frac{3}{4}-81\right)\left(\frac{3^2}{5}-81\right)....0....\left(\frac{3^{2000}}{2003}-81\right)\)
\(=0\)