A=1+2+2²+2³+...+2⁶²+2⁶³

2A=2+2²+2³+2⁴+...+2⁶³+2⁶⁴

2A-A=2+2²+2³+2⁴+...+2⁶³+2⁶⁴-1+2+2²+2³+...+2⁶²+2⁶³

A=2⁶⁴-1

\(A=1+2+2^2+2^3+..+2^{62}+2^{63}\)

\(2A=2+2^2+2^3+...+2^{63}+2^{64}\)

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

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

A=1+2+2²+2³+...+2⁶²+2⁶³

2A=2(1+2+2²+2³+...+2⁶²+2⁶³)

2A=2+2³+2⁴+2⁵...+2⁶³+2⁶⁴

2A-A=(2+2³+2⁴+2⁵...+2⁶³+2⁶⁴)-(1+2+2²+2³+...+2⁶²+2⁶³)

A=2⁶⁴-1

Nha bạn. Chúc bn ht

A = 1 + 2 + 2² + 2³ + ... + 2⁶² + 2⁶³

2A = 2 + 2² + 2³ + 2⁴ + ... + 2⁶³ + 2⁶⁴

A = 2⁶⁴ - 1

tính như nào nhỉ

`1+2+2^2+2^3+....+2^63`

`=2+2+2^2+2^3+....+2^63-1`

`=2.2+2^2+2^3+....+2^63-1`

`=2^2+2^2+2^3+....+2^63-1`

`=2.2^2+2^3+....+2^63-1`

`=2^3+2^3+...2^63-1`

`=2.2^3+....+2^63-1`

`=2^4+....+2^63-1`

`=2^{63}.2-1=2^64-1`

Đặt \(A=1+2+2^2+2^3+...+2^{63}\)

\(\Rightarrow2A=2+2^2+2^3+2^4+2^5+...+2^{64}\)

\(\Rightarrow A=2A-A=\left(2+2^2+2^3+2^4+...+2^{64}\right)-\left(1+2+2^2+2^3+...+2^{63}\right)=2^{64}-1\left(đpcm\right)\)

\(S_1=1+2+2^2+2^3+..+2^{63}\\ \Rightarrow2S_1=2+2^2+2^3+2^4+...+2^{64}\\ \Rightarrow S_1-2S_1=1-2^{64}\\ \Rightarrow-S_1=1-2^{64}\\ \Rightarrow S_1=2^{64}-1.\)

- Ta có: S₁ = 1 + 2 + 2² + 2³ + … + 2⁶³ = 1 + 2(1 + 2 + 2² + 2³ + … + 2⁶²) (1)

= 1 + 2(S₁ - 2⁶³) = 1 + 2S₁ - 2⁶⁴ S₁ = 2⁶⁴ - 1

H2.right

`#3107.101107`

`S_1 = 1 + 2 + 2^2 + 2^3 + ... + 2^63`

`2S_1 = 2 + 2^2 + 2^3 + .... + 2^64`

`2S_1 - S_1 = (2 + 2^2 + 2^3 + ... + 2^64) - (1 + 2 + 2^2 + 2^3 + ... + 2^63)`

`S_1 = 2 + 2^2 + 2^3 + ... + 2^64 - 1 - 2 - 2^2 - 2^3 - ... - 2^63`

`S_1 = 2^64 - 1`

Vậy, `S_1 = 2^64 - 1.`

làm gì đấy bạn

a) 23 + (-77) + (-23) + 77 =
[23 + (-23)] + [(-77) + 77]
= …0+0=0……
b) (-2 020) + 2 021 + 21 + (-22)
=[(-2 020) + 2 021] + [21 + (-22)]
= …1……+ (-1)……..
= 0. 

a) 23 + (-77) + (-23) + 77 =
[23 + (-23)] + [(-77) + 77]
= …0+0=0……
b) (-2 020) + 2 021 + 21 + (-22)
=[(-2 020) + 2 021] + [21 + (-22)]
= …1……+ (-1)……..
= 0. 

cau 1:b,cau2d,cau3b

b,d,d

thứ tự 1,2,3

a: \(\left(-17\right)+5+\left(-8\right)+17\)

\(=\left(-17+17\right)+\left(5-8\right)\)

=0-3

=-3

b: \(\left(-9\right)+\left(-11\right)+21+\left(-1\right)\)

\(=\left(-9-1\right)+\left(21-11\right)\)

=10-10

=0

c: \(15+23+\left(-25\right)+\left(-23\right)\)

\(=\left(15-25\right)+\left(23-23\right)\)

=-10+0

=-10

d: \(\left(-3\right)+\left(-350\right)+\left(-7\right)+350\)

\(=\left(-3-7\right)+\left(-350+350\right)\)

=-10+0

=-10

e: \(\left(-3\right)+\left(-250\right)+\left(-7\right)+250\)

\(=\left(-3-7\right)+\left(-250+250\right)\)

=-10+0

=-10

f: \(\left(-4\right)+\left(-440\right)+\left(-6\right)+440\)

\(=\left(-4-6\right)+\left(-440+440\right)\)

=-10+0

=-10

g: \(483+\left(-56\right)+263+\left(-64\right)\)

\(=\left(483+263\right)+\left(-56-64\right)\)

\(=746-110=636\)

h: \(215+43+\left(-215\right)+\left(-25\right)\)

\(=\left(215-215\right)+\left(43-25\right)\)

=0+18

=18

a. (-17) + 5 + (-8) + 17

= [5 + (-8)] + [(-17) + 17]

= -3

b. (-9) + (-11) + 21 + (-1)

= [(-9) + (-1)] + [21 + (-11)]

= -10 + 10

= 0

c. 15 + 23 + (-25) + (-23)

= [15 + (-25)] + (23 - 23)

= -10

d. (-3) + (-350) + (-7) + 350

= [(-3) + (-7)] + [(-350) + 350]

= -10

e. (-3) + (-250) + (-7) + 250

= [(-3) + (-7)] + [(-250) + 250]

= -10

f. (-4) + (-440) + (-6) + 440

= [(-4) + (-6)] + [(-440) + 440]

= -10

g. 483 + (-56) + 263 + (-64)

= (483 + 263) + [(-56) + (-64)]

= 746 + (-120)

= 626

h. 215 + 43 + (-215) + (-25)

= [215 + (-215)] + [43 + (-25)]

= 18

a) (-17) + 5 + (-8) + 17

= [5 + (-8)] + [(-17) + 17]

= -3

b) (-9) + (-11) + 21 + (-1)

= [(-9) + (-1)] + [21 + (-11)]

= -10 + 10

= 0

c) 15 + 23 + (-25) + (-23)

= [15 + (-25)] + (23 - 23)

= -10

d) (-3) + (-350) + (-7) + 350

= [(-3) + (-7)] + [(-350) + 350]

= -10

e) (-3) + (-250) + (-7) + 250

= [(-3) + (-7)] + [(-250) + 250]

= -10

f) (-4) + (-440) + (-6) + 440

= [(-4) + (-6)] + [(-440) + 440]

= -10

g) 483 + (-56) + 263 + (-64)

= (483 + 263) + [(-56) + (-64)]

= 746 + (-120)

= 626

h) 215 + 43 + (-215) + (-25)

= [215 + (-215)] + [43 + (-25)]

= 18

a, \(\dfrac{7}{22}\) - \(\dfrac{15}{23}\) + \(\dfrac{2022}{2023}\) - \(\dfrac{8}{23}\) + \(\dfrac{15}{22}\)

= ( \(\dfrac{7}{22}\) + \(\dfrac{15}{22}\)) - ( \(\dfrac{15}{23}+\dfrac{18}{23}\)) + \(\dfrac{2022}{2023}\)

= \(\dfrac{22}{22}\) - \(\dfrac{23}{23}\) + \(\dfrac{2022}{2023}\)

= 1 - 1 + \(\dfrac{2022}{2023}\)

= \(\dfrac{2022}{2023}\) 

b, - \(\dfrac{2}{11}\) + 5\(\dfrac{5}{6}\) ( 14\(\dfrac{1}{5}\) - 11\(\dfrac{1}{5}\)): 5\(\dfrac{1}{2}\)

= - \(\dfrac{2}{11}\) + \(\dfrac{35}{6}\) ( \(\dfrac{71}{5}\) - \(\dfrac{56}{5}\)) : \(\dfrac{11}{2}\)

= - \(\dfrac{2}{11}\) + \(\dfrac{35}{6}\) . \(\dfrac{15}{5}\) : \(\dfrac{11}{2}\)

= - \(\dfrac{2}{11}\) + \(\dfrac{35}{2}\) \(\times\) \(\dfrac{2}{11}\)

= - \(\dfrac{2}{11}\) + \(\dfrac{35}{11}\)

= \(\dfrac{33}{11}\)

= 3 

c, 2000 + { 20 - [ 4.2022⁰ - (3² + 5):2] }

= 2000 + { 20 - [ 4.1 - (9+5):2]}

= 2000 + { 20 - [ 4 - 14 : 2 ]}

= 2000 + { 20 - [ 4 -7]}

= 2000 + { 20 - (-3)}

= 2000 + 23

= 2023

Bài 1

S₂ = 21 + 23 + 25 + ... + 1001

Số số hạng của S₂:

(1001 - 21) : 2 + 1 = 491

⇒ S₂  = (1001 + 21) . 491 : 2 = 250901

--------

S₄  = 15 + 25 + 35 + ... + 115

Số số hạng của S₄:

(115 - 15) : 10 + 1 = 11

⇒ S₄ = (115 + 15) . 11 : 2 = 715

Bài 2

a) 2x - 138 = 2³.3²

2x - 138 = 8.9

2x - 138 = 72

2x = 72 + 138

2x = 210

x = 210 : 2

x = 105

b) 5.(x + 35) = 515

x + 35 = 515 : 5

x + 35 = 103

x = 103 - 35

x = 78

c) 814 - (x - 305) = 712

x - 305 = 814 - 712

x - 305 = 102

x = 102 + 305

x = 407

d) 20 - [7.(x - 3) + 4] = 2

7(x - 3) + 4 = 20 - 2

7(x - 3) + 4 = 18

7(x - 3) = 18 - 4

7(x - 3) = 14

x - 3 = 14 : 7

x - 3 = 2

x = 2 + 3

x = 5

e) 9ˣ⁻¹ = 9

x - 1 = 1

x = 1 + 1

x = 2

2:

a: \(2x-138=2^3\cdot3^2\)

=>\(2x-138=8\cdot9=72\)

=>2x=138+72=210

=>x=105

b: \(5\cdot\left(x+35\right)=515\)

=>x+35=103

=>x=103-35=68

c: \(814-\left(x-305\right)=712\)

=>x-305=814-712=102

=>x=102+305=407

d: \(20-\left[7\left(x-3\right)+4\right]=2\)

=>7(x-3)+4=18

=>7(x-3)=14

=>x-3=2

=>x=5

e: \(9^{x-1}=9\)

=>x-1=1

=>x=2

f: \(5^{x-2}-3^2=2^4-\left(2^8\cdot2^2-2^{10}\cdot2^2\right)\)

=>\(5^{x-2}-9=16-1024+4096\)

=>\(5^{x-2}=3097\)

=>\(x-2=log_53097\)

=>\(x=2+log_53097\)