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10 tháng 8 2023

7) \(A=1^2-2^2+3^2-4^2+...-2004^2+2005^2\)

\(A=\left(-1\right)\left(1^{ }+2\right)+\left(-1\right)\left(3+4\right)+...+\left(-1\right)\left(2003+2004\right)+2005^2\)

\(A=-\left(1+2+3+...+2004\right)+2005^2\)

\(A=-\dfrac{2004.\left(2004+1\right)}{2}+2005^2\)

\(A=-1002.2005+2005^2\)

\(A=2005\left(2005-1002\right)=2005.1003=2011015\)

10 tháng 8 2023

8) \(B=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(B=\dfrac{\left(2^2-1\right)}{2-1}\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(B=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(B=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(B=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(B=\left(2^{32}-1\right)\left(2^{32}+1\right)-2^{64}\)

\(B=\left(2^{64}-1\right)-2^{64}\)

\(B=-1\)

17 tháng 9 2018

A = 12 – 22 + 32 – 42 + … – 20042 + 20052

     A = 1 + (32 – 22) + (52 – 42)+ …+ ( 20052 – 20042)

     A = 1 + (3 + 2)(3 – 2) + (5 + 4 )(5 – 4) + … + (2005 + 2004)(2005 – 2004)

     A = 1 + 2 + 3 + 4 + 5 + … + 2004 + 2005

     A = ( 1 + 2002 ). 2005 : 2 = 2011015

b/  B = (2 + 1)(22 +1)(24 + 1)(28 + 1)(216 + 1)(232 + 1) – 264

     B = (22  - 1) (22 +1)(24 + 1)(28 + 1)(216 + 1)(232 + 1) – 264

     B = ( 24 – 1)(24 + 1)(28 + 1)(216 + 1)(232 + 1) – 264

     B = …

     B =(232 - 1)(232 + 1) – 264

     B = 264 – 1 – 264

     B = - 1

17 tháng 9 2018

xin lỗi nha chỗ câu a mình lộn

chỗ (1+2002)x2005:2=2011015 là sai nha 

       (1+2005)x2005:2= 2011015 là đúng nha 

17 tháng 6 2018

Giúp TT

17 tháng 6 2018

a,A=-(12-22+32-42+...+992-1002)

=-[(1-2)(1+2)+(3-4)(3+4)+...+(99-100)(99+100)]

=-[(-1).3+(-1).7+...+(-1).199]

=-[(-1).(3+7+...+199]

=\(\frac{\left(199+3\right).50}{2}=5050\)

b, tương tự a

c) C=1(2+1)(22+1)(24+1)(28+1)(216+1)(232+1)-264

=(2-1)(2+1)(22+1)(24+1)(28+1)(216+1)(232+1)-264

=(22-1)(22+1)(24+1)(28+1)(216+1)(232+1)-264

=(24-1)(24+1)(28+1)(216+1)(232+1)-264

=(28-1)(28+1)(216+1)(232+1)-264

=(216-1)(216+1)(232+1)-264

=(232-1)(232+1)-264

=264-1-264

=-1

AH
Akai Haruma
Giáo viên
22 tháng 9 2020

a)

$A=(1^2-2^2)+(3^2-4^2)+....+(2003^2-2004^2)+2005^2$

$=(1-2)(1+2)+(3-4)(3+4)+....+(2003-2004)(2003+2004)+2005^2$

$=-(1+2)-(3+4)-...-(2003+2004)+2005^2$

$=-(1+2+3+...+2004)+2005^2=-\frac{2004.2005}{2}+2005^2$

$=2005^2-1002.2005=2005(2005-1002)=2011015$

b)

$B=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^{16}+1)(2^{32}+1)-2^{64}$

$=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^{16}+1)(2^{32}+1)-2^{64}$

$=(2^4-1)(2^4+1)(2^8+1)(2^{16}+1)(2^{32}+1)-2^{64}$

$=(2^8-1)(2^8+1)(2^{16}+1)(2^{32}+1)-2^{64}$

$=(2^{16}-1)(2^{16}+1)(2^{32}+1)-2^{64}$

$=(2^{32}-1)(2^{32}+1)-2^{64}$

$=2^{64}-1-2^{64}=-1$

AH
Akai Haruma
Giáo viên
22 tháng 9 2020

c) Do $x=16$ nên $x-16=0$

$R(x)=x^4-17x^3+17x^2-17x+20$

$=(x^4-16x^3)-(x^3-16x^2)+x^2-16x-x+20$

$=x^3(x-16)-x^2(x-16)+x(x-16)-x+20$

$=x^3.0-x^2.0+x.0-x+20=-x+20=-16+20=4$

d) Do $x=12$ nên $x-12=0$. Khi đó:

$S(x)=(x^{10}-12x^9)-(x^9-12x^8)+(x^8-12x^7)-....+(x^2-12x)-x+10$

$=x^9(x-12)-x^8(x-12)+x^7(x-12)-....+x(x-12)-x+10$

$=(x-12)(x^9-x^8+x^7-....+x)-x+10$

$=0-x+10=-x+10=-12+10=-2$

b) Ta có: \(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(=\left(2+1\right)\left(2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)

\(=\left(2^{32}-1\right)\left(2^{32}+1\right)-2^{64}\)

\(=2^{64}-1-2^{64}=-1\)

11 tháng 10 2016

A = (2 + 1)(22 + 1)(24 + 1)(28 + 1)(216 + 1)(232 + 1) - 264

A = (2 - 1)(2 + 1)(22 + 1)(24 + 1)(28 + 1)(216 + 1)(232 + 1) - 264

A = (22 - 1)(22 + 1)(24 + 1)(28 + 1)(216 + 1)(232 + 1) - 264

A = (24 - 1)(24 + 1)(28 + 1)(216 + 1)(232 + 1) - 264

A = (28 - 1)(28 + 1)(216 + 1)(232 + 1) - 264

A = (216 - 1)(216 + 1)(232 + 1) - 264

A = (232 - 1)(232 + 1) - 264

A = 264 - 1 - 264

A = -1

17 tháng 8 2019

Đặt \(A=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)

\(\Rightarrow A=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)

\(\Rightarrow A=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)

\(\Rightarrow A=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)

\(\Rightarrow A=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)

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

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

\(\Rightarrow A=2^{64}-1\)

\(\Rightarrow B=2^{64}-1-2^{64}=-1\)

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 :

\(2^{64}-1-2^{64}=-1\)

25 tháng 5 2018

Phải là (2+1)(2²+1)(2⁴+1)...(2³²+1)- 2^64

(2+1)(2²+1)(2⁴+1)...(2³²+1)

=(2-1)(2+1)(2²+1)(2⁴+1)...(2³²+1)

=(2²-1)(2²+1)(2⁴+1)...(2³²+1)

=(2⁴-1)(2⁴+1)...(2³²+1)=…=2^64-1

Vậy C=-1