\(A=1+2+2^2+...+2^{2018}\)

\(2A=2+2^3+2^4+...+2^{2019}\)

\(A=2A-A=1-2^{2019}\)

\(B-A=2^{2019}-\left(1-2^{2019}\right)\)

\(B-A=2^{2019}-1+2^{2019}\)

\(B-A=1\)

`#3107`

\(A=1+2+2^2+2^3+...+2^{2018}\) và \(B=2^{2019}\)

Ta có:

\(A=1+2+2^2+2^3+...+2^{2018}\)

\(2A=2+2^2+2^3+...+2^{2019}\)

\(2A-A=\left(2+2^2+2^3+...+2^{2019}\right)-\left(1+2+2^2+2^3+...+2^{2018}\right)\)

\(A=2+2^2+2^3+...+2^{2019}-1-2-2^2-2^3-...-2^{2018}\)

\(A=2^{2019}-1\)

Vậy, \(A=2^{2019}-1\)

Ta có:

\(B-A=2^{2019}-2^{2019}+1=1\)

Vậy, `B - A = 1.`

a: \(61\cdot45+61\cdot23-68\cdot51\)

\(=61\left(45+23\right)-68\cdot51\)

\(=68\cdot61-68\cdot51\)

\(=68\left(61-51\right)=68\cdot10=680\)

b: \(3\cdot5^2-\left(75-4\cdot2^3\right)\)

\(=75-75+4\cdot8\)

\(=4\cdot8=32\)

c: \(36:\left\{2^2\cdot5-\left[30-\left(5-1\right)^2\right]\right\}\)

\(=\dfrac{36}{20-30+4^2}\)

\(=\dfrac{36}{-10+16}=\dfrac{36}{6}=6\)

d: \(\left(12\cdot49-3\cdot2^2\cdot7^2\right):\left(2020\cdot2021\right)\)

\(=\dfrac{\left(12\cdot49-12\cdot49\right)}{2020\cdot2021}=0\)

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

a: \(17\cdot85+15\cdot17-120\)

\(=17\left(85+15\right)-120\)

=1700-120

=1580

b: \(2^3\cdot17-2^3\cdot14\)

\(=2^3\left(17-14\right)\)

\(=8\cdot3=24\)

c: \(20-\left\lbrack30-\frac{\left(5-1\right)^2}{2}\right\rbrack\)

\(=20-30+\frac{4^2}{2}\)

\(=-10+\frac{16}{2}=-10+8=-2\)

d: \(80-\left(4\cdot5^2-3\cdot2^2\right)\)

\(=80-\left(4\cdot25-3\cdot4\right)\)

=80-100+12

=92-100

=-8

e: \(27\cdot77+24\cdot27-27\)

\(=27\left(77+24-1\right)\)

\(=27\cdot100=2700\)

f: \(174:\left\lbrace2\cdot\left\lbrack36+\left(4^2-23\right)\right\rbrack\right\rbrace\)

\(=\frac{174}{2\cdot\left(36+16-23\right)}=\frac{87}{52-23}=\frac{87}{29}=3\)

a: \(\frac{7}{22}+\frac{-15}{23}+\frac{2022}{2023}+\frac{-8}{23}+\frac{15}{22}\)

\(=\left(\frac{7}{22}+\frac{15}{22}\right)+\left(-\frac{15}{23}-\frac{8}{23}\right)+\frac{2022}{2023}\)

\(=1-1+\frac{2022}{2023}=\frac{2022}{2023}\)

b: \(-\frac{2}{11}+5\frac56\left(14\frac15-11\frac15\right):5\frac12\)

\(=-\frac{2}{11}+\frac{35}{6}\left(14+\frac15-11-\frac15\right):\frac{11}{2}\)

\(=\frac{-2}{11}+\frac{35}{6}\cdot\frac{2}{11}\cdot3=\frac{-2}{11}+\frac{35}{11}=\frac{33}{11}=3\)

c: \(2000+\left\lbrace20-\left\lbrack4\cdot2022^0-\left(3^2+5\right):2\right\rbrack\right\rbrace\)

\(=2000+20-\left\lbrack4\cdot1-14:2\right\rbrack\)

=2020-(4-7)

=2020-(-3)

=2023

a) \(3.5^2+15.2^2-26\div2\)

= 3.25 + 15.4 - 13

= 75 + 60 - 13

= 135 - 13

= 122

b) \(5^3.2-100\div4+2^3.5\)

= 125.2 - 25 + 8.5

= 250 - 25 + 40

= 225 + 40

= 265

c)\(6^2\div9+50.2-3^3.33\)

= 36 : 9 + 100 - 9.33

= 4 + 100 - 297

= 104 - 297

= -193

d)\(3^2.5+2^3.10-81\div3\)

= 9.5 + 8.10 - 27

= 45 + 80 - 27

= 125 - 27

= 98

e) \(5^{13}\div5^{10}-25.2^2\)

= 5³ - 25.4

= 125 - 100

= 25

f) \(20\div2^2+5^9\div5^8\)

= 20 : 4 + 5

= 5 + 5

= 10

Bài 2 : 

a, \(x=\dfrac{3}{5}-\dfrac{7}{8}=\dfrac{24-30}{40}=-\dfrac{6}{40}=-\dfrac{3}{20}\)

b, \(2x-1=-2\Leftrightarrow x=-\dfrac{1}{2}\)

`a)3/5+(-4/9)`

`=3/5-4/9`

`=27/45-20/45`

`=7/45`

`b)3/5+2/5 . 15/8`

`=3/5 + 30/40`

`=3/5+3/4`

`=12/20+15/20`

`=27/20`

`c)7/2 . 8/13 + 8/13 . (-5/2)`

`=8/13 . (7/2 +(-5)/2)`

`=8/13 . 1`

`=8/13`

`d)-5/17 . (-9/23)+9/23 . (-22/17) + 11 9/23`

`=-5/17 . (-9/23) + 9/23 . (-1) . 22/17 + 11 + 9/23`

`=-5/17 . (-9/23) + (-9/23) . 22/17+11+9/23`

`= -9/23 ( -5/17 + 22/17)+11+9/23`

`= - 9/23 . 1+11+9/23`

`=-9/23+11+9/23`

`=(-9/23+9/23)+11`

`=0+11`

`=11`

a: =27/45-20/45=7/45

b: =3/5+30/40

=3/5+3/4

=12/20+15/20

=27/20

c: =8/13(7/2-5/2+1)=8/13*2=16/13

d: =9/23*5/17-9/23*22/17+11+9/23

=-9/23+11+9/23

=11