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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 + 22 + 23 + ... + 262 + 263
2A = 2 + 22 + 23 + 24 + ... + 263 + 264
A = 264 - 1
`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`
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: \(\left(-17\right)+5+\left(-8\right)+17\)
\(=\left(-17+17\right)+\left(5-8\right)\)
=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, \(\dfrac{7}{22}\) - \(\dfrac{15}{23}\) + \(\dfrac{2022}{2023}\) - \(\dfrac{8}{23}\) + \(\dfrac{15}{22}\)
= ( \(\dfrac{7}{22}\) + \(\dfrac{15}{22}\)) - ( \(\dfrac{15}{23}+\dfrac{18}{23}\)) + \(\dfrac{2022}{2023}\)
= \(\dfrac{22}{22}\) - \(\dfrac{23}{23}\) + \(\dfrac{2022}{2023}\)
= 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
A=1+2+22+23+....+263
2A=2+22+23+....+263+264
2A-A=2+22+23+....+263+264-(1+2+22+23+....+263)
A=264-1
A = 1 + 2 + 22 + 23 + ... + 263
2A = 2 + 22 + ... + 264
2A - A = 264 - 1
A = 264 - 1