Question

So sánh :

A =  ( 3 + 1 ) ( 3² + 1 ) ( 3⁴ + 1) ( 3⁸ + 1 ) ( 3¹⁶ + 1 )

và B = 3³²  - 1

Answer 1

Ta có :

\(2A=\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

\(\Rightarrow2A=3^{32}-1\)

\(\Rightarrow A=\frac{3^{32}-1}{2}< 3^{32}-1\)

=> A < B 

Answer 2

A = (3 + 1).(3² + 1).(3⁴ + 1).(3⁸ + 1).(3¹⁶ + 1)

2A = (3 - 1).(3 + 1).(3² + 1).(3⁴ + 1).(3⁸ + 1).(3¹⁶ + 1)

2A = (3² - 1).(3² + 1).(3⁴ + 1).(3⁸ + 1).(3¹⁶ + 1)

2A = (3⁴ - 1).(3⁴ + 1).(3⁸ + 1).(3¹⁶ + 1)

2A = (3⁸ - 1).(3⁸ + 1).(3¹⁶ + 1)

2A = (3¹⁶ - 1).(3¹⁶ + 1)

2A = 3³² - 1 = B

=> A < B

Answer 3

A =  ( 3 + 1 ) ( 3² + 1 ) ( 3⁴ + 1) ( 3⁸ + 1 ) ( 3¹⁶ + 1 )

2A=(3-1)(3+1)(3²+1)(3⁴+1)(3⁸+1)(3¹⁶+1)=B

=>A<B

 

Answer 4

thiếu 1 số số