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LM
1
30 tháng 11 2022
\(\dfrac{1}{1-x}+\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{1+x+1-x}{1-x^2}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{2+2x^2+2-2x^2}{1-x^4}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{4+4x^4+4-4x^4}{1-x^8}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{8+8x^8+8-8x^8}{1-x^{16}}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{16+16x^{16}+16-16x^{16}}{1-x^{32}}=\dfrac{32}{1-x^{32}}\)
DN
30 tháng 7 2018
\(3.\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
=\(\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
=\(\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
=\(\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
=\(\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
=\(\left(2^{32}-1\right)\left(2^{32}+1\right)\)
=\(2^{64}-1\)
TN
1
15 tháng 7 2016
\(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Leftrightarrow\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Leftrightarrow\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Leftrightarrow\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Leftrightarrow\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Leftrightarrow\left(2^{32}-1\right)\left(2^{32}+1\right)\)
\(\Leftrightarrow2^{64}-1\)
TN
1
13 tháng 8 2021
Ta có: \(A=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\)
\(=2^{32}-1< 2^{32}\)
\(\Leftrightarrow A< B\)
MT
26 tháng 6 2015
(2+1)(2^2+1)(2^4 +1)(2^8+1)(2^16+1) - 2^32
=1.(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
=-1
26 tháng 6 2015
(2+1 ) ( 2^2 + 1) ... (2^16 + 1) - 2^32
= 3 ( 2^2 + 1) ....( 2^16 + 1) -2^32
= ( 2^2 - 1)( 2^2 +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
1 tháng 8 2016
VT=[(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)]/2
=[(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)]/2
=[(2^4-1(2^4+1)(2^8+1)(2^16+1)]/2
=[(2^8-1)(2^8+1)(2^16+1)]/2
=[(2^16-1)(2^16+1)]/2
=(2^32-1)/2
HN
2