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21 tháng 9 2016
(2 + 1)(22 + 1)(24 + 1)(28 + 1)(216 + 1) - 232
= (2 - 1)(2 + 1)(22 + 1)(24 + 1)(28 + 1)(216 + 1) - 232
= (22 - 1)(22 + 1)(24 + 1)(28 + 1)(216 + 1) - 232
= (24 - 1)(24 + 1)(28 + 1)(216 + 1) - 232
= (28 - 1)(28 + 1)(216 + 1) - 232
= (216 - 1)(216 + 1) - 232
= (232 - 1) - 232
= 232 - 1 - 232
= -1
NT
1
30 tháng 7 2018
\(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=2^{32}-1\)
KB
31 tháng 10 2018
Ta có : \(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)-2^{32}\)
\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)-2^{32}\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)-2^{32}\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)-2^{32}\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)-2^{32}\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)-2^{32}\)
\(=\left(2^{32}-1\right)-2^{32}\)
\(=-1\)
31 tháng 10 2018
(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)-2^32=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)-2^32
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)-2^32=(2^4-1)(2^4+1)(2^8+1)(2^16+1)-2^32
=(2^8-1)(2^8+1)(2^16+1)-2^32=(2^16-1)(2^16+1)-2^32=2^32-1-2^32=-1
NM
2
AT
23 tháng 6 2017
Ta có:
\(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2+1\right)\left(2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\)
\(=2^{32}-1\)
Vậy...
NT
1
DN
24 tháng 10 2018
\(A=3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=\left(2^{32}-1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=2^{64}-1\)
Vậy \(A=2^{64}-1\)
NT
1
5 tháng 11 2018
\(A=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(A=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(A=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(A=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(A=\left(2^{32}-1\right)\left(2^{32}+1\right)\)
\(A=2^{64}-1\)
ND
2
2T
17 tháng 8 2019
Đặt \(A=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=\left(2^{32}-1\right)\left(2^{32}+1\right)\)
\(\Rightarrow A=2^{64}-1\)
\(\Rightarrow B=2^{64}-1-2^{64}=-1\)
N
17 tháng 8 2019
Ta có : \(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^{32}-1\right)\left(2^{32}+1\right)=2^{64}-1\)
Thay 264 - 1 vào B, ta được :
\(2^{64}-1-2^{64}=-1\)
Nhân với 2-1 áp dụng bất đẳng thức a^2-b^2=(a-b)(a+b)
=> 2^64-1
(2+1)(22+1)(24+1)(28+1)(216+1)(232+1)
=[3(22+1)(24+1)](28+1)(216+1)(232+1)
=[(22-1)(22+1)](24+1)(28+1)(216+1)(232+1)
=[(24-1)(24+1)](28+1)(216+1)(232+1)
=[(28-1)(28+1)](216+1)(232+1)
=[(216-1)(216+1)](232+1)
=(232-1)(232+1)