Question

[Trần Thị Thúy Hiền]

So sánh hai số : 

A= (2+1).(2²+1).(2⁴+1).(2⁸+1).(2¹⁶+1)

và B= 2³²

Answer 1

[Trần Việt Linh]

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

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

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

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

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

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

\(B=2^{32}\)

=> \(A< B\)

Answer 2

[Nguyễn Phương HÀ]

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