(3/4-81)(32/5-81)(33/6-81)...(32016/2019-81)
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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
KV
3 tháng 12 2023
a) (38 - 60) + (20 - 38)
= 38 - 60 + 20 - 38
= (38 - 38) + (-60 + 20)
= 0 - 40
= -40
b) 75 - (20 + 75)
= 75 - 20 - 75
= (75 - 75) - 20
= 0 - 20
= -20
c) 32 + (60 - 32)
= 32 + 60 - 32
= (32 - 32) + 60
= 0 + 60
= 60
d) (81 - 36) - (81 - 36)
= 81 - 36 - 81 + 36
= (81 - 81) + (-36 + 36)
= 0 + 0
= 0
e) (2 + 4 + 6 + 8) - (1 + 3 + 5 + 7)
= 2 + 4 + 6 + 8 - 1 - 3 - 5 - 7
= (2 - 1) + (4 - 3) + (6 - 5) + (8 - 7)
= 1 + 1 + 1 + 1
= 4
f) (1 + 3 + 5 + 7 + ... + 99) - (2 + 4 + 6 + 8 + ... + 100)
= 1 + 3 + 5 + 7 + ... + 99 - 2 - 4 - 6 - 8 - ... - 100
= (1 - 2) + (3 - 4) + (5 - 6) + (7 - 8) + ... + (99 - 100)
= -1 - 1 - 1 - 1 - ... - 1 (50 chữ số 1)
= -50