Tính:\(\frac{69}{157}-\)(2+(3+(4+5-1)-1)-1)
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NT
1
13 tháng 10 2018
\(\frac{69}{157}-\left\{2+\left[3+\left(4+5^{-1}\right)^{-1}\right]^{-1}\right\}^{-1}\)
\(=\frac{69}{157}-\left\{2+\left[3+\left(4+\frac{1}{5}\right)^{-1}\right]^{-1}\right\}^{-1}\)
\(=\frac{69}{157}-\left\{2+\left[3+\left(\frac{21}{5}\right)^{-1}\right]^{-1}\right\}^{-1}\)
\(=\frac{69}{157}-\left[2+\left(3+\frac{5}{21}\right)^{-1}\right]^{-1}\)
\(=\frac{69}{157}-\left[2+\left(\frac{68}{21}\right)^{-1}\right]^{-1}\)
\(=\frac{69}{157}-\left(2+\frac{21}{68}\right)^{-1}\)
\(=\frac{69}{157}-\left(\frac{157}{68}\right)^{-1}\)
\(=\frac{69}{157}-\frac{68}{157}\)
\(=\frac{1}{157}\)
KN
1
13 tháng 7 2019
69/157 - (2 + (3 + (4 + 5-1)-1)-1)-1
= 69/157 - (2 + 21/68)-1
= 69/157 - (157/68)-1
= 69/157 - 68/157
= 1/157
KN
1
H
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: \(\dfrac{69}{157}-\left(2+\left(3+4+5^{-1}\right)^{-1}\right)^{-1}\)
\(=\dfrac{69}{157}-\left(2+\left(3+4+\dfrac{1}{5}\right)^{-1}\right)^{-1}\)
\(=\dfrac{69}{157}-\left(2+1:\dfrac{36}{5}\right)^{-1}\)
\(=\dfrac{69}{157}-\left(2+\dfrac{5}{36}\right)^{-1}\)
\(=\dfrac{69}{157}-\left(\dfrac{77}{36}\right)^{-1}\)
\(=\dfrac{69}{157}-\dfrac{36}{77}=\dfrac{-339}{12089}\)
S
1
5 tháng 4 2020
\(\frac{69}{157}-\left(2+\left(3+4+5^{-1^{-1^{-1^{-1}}}}\right)\right)\)
\(=\frac{69}{157}-\left(2+\left(3+4+\frac{1}{5}\right)\right)\)
\(=\frac{69}{157}-\left(2+\frac{36}{5}\right)\)
\(=\frac{69}{157}-\frac{46}{5}\)
\(=\frac{-6877}{785}\)
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