Question

So sánh hai số : 

A= (2+1).(2²+1).(2⁴+1).(2⁸+1).(2¹⁶+1)

và B= 2³²

Answer 1

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

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

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

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

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

\(=\left(2^{16}-1\right)\left(2^{16}+1\right)=2^{32}-1\)

\(B=2^{32}\)

=> \(A< B\)

Answer 2

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

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

=\(2^{32}-1\)    (ấp dụng các hằng đẳng thức )

=> A=2³²-1

B=2³²

=> A<B

Answer 3

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

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

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

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

=..............................................................

\(=\left(2^{16}-1\right)\left(2^{16}+1\right)=2^{32}-1\)

=> A < B

Answer 4

A = (2 + 1) (2² + 1) ( 2⁴+ 1) ( 2⁸+ 1) ( 2¹⁶+ 1)

= (2 − 1)(2 + 1) (2² + 1) ( 2⁴+ 1) ( 2⁸+ 1) ( 2¹⁶+ 1)

= (2² − 1) ( 2²+ 1) ( 2⁴+ 1) ( 2⁸+ 1) ( 2¹⁶+ 1)

= (2⁴ − 1) ( 2⁴+ 1) ( 2⁸+ 1) ( 2¹⁶+ 1) 

=( 2⁸ -1) (2⁸+1) (2¹⁶ +1 )

=( 2¹⁶ -1) (2¹⁶ +1)

=2³²-1

=>A<B

Answer 5

A < B