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Gọi A là biểu thức ta có:
CÂU1 :A = 1.2+2.3+3.4+......+99.100
3A = 1.2.3 + 2.3.3 + 3.4.3 + … + 99.100.3
3A = 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98)
3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100
3A = 99.100.101
A = 99.100.101 : 3
A = 33.100.101
A = 333 300

a) 12 - (8 . 22 - 4 . 23)
= 12 - (4 . 2 . 22 - 4 . 23)
= 12 - (4 . 23 - 4 . 23)
= 12 - 0
= 12
b) 56 : 54 + 22 . 23
= 52 + 25
= 25 + 32
= 57
c) 28 . 76 + 35 . 28 - 11 . 28
= 28 (76 + 35 - 28)
= 28 .100
= 2800
d) 3. 42 - 62 :2
= 3. 16 - 36 :2
= 48 - 18
= 30
e) 13 . 42 + 13 . 58 - 50 : (32 + 42)
= 13 . 42 + 13 . 58 - 50 : (9+ 16)
= 13 . (42 + 58) - 50 : (9+ 16)
= 13 .100 - 50 : 25
= 1300 - 2
= 1298
g) 34 : 32 + 2 . 23
= 32 + 24
= 9 + 16
= 25
HỌC TỐT

\(2b)\)
Đặt :
\(S=1+4+4^2+4^3+4^4....................+4^{100}\)
\(4S=4\left(1+4+4^2+4^3+4^4+.............+4^{100}\right)\)
\(4S=4+4^2+4^3+4^4+4^4+.......+4^{101}\)
\(4S-S=\left(4+4^2+4^3+4^4+4^5+.......+4^{101}\right)-\left(1+4+4^2+4^3+4^4+...............+4^{100}\right)\)
\(3S=4^{101}-1\)
\(S=\dfrac{4^{101}-1}{3}\)

(1.2 + 2.3 + 3.4 + ... + 2012.2013) - (22 + 32 + 42 + 52 + ... + 20132)
= [(2 - 1).2 + (3 - 1).3 + (4 - 1).4 + ... + (2013 - 1).2013] - (22 + 32 + 42 + 52 + ... + 20132)
= (22 - 2 + 32 - 3 + 42 - 4 + ... + 20132 - 2013) - (22 + 32 + 42 + 52 + ... + 20132)
= 22 - 2 + 32 - 3 + 42 - 4 + ... + 20132 - 2013 - 22 - 32 - 42 - 52 - ... - 20132
= (22 - 22) + (32 - 32) + (42 - 42) + ... + (20132 - 20132) - (2 + 3 + 4 + ... + 2013)
= 0 - (2 + 3 + 4 + ... + 2013)
= 0 - (1 + 2 + 3 + 4 + ... + 2013) + 1
= 0 - \(\dfrac{2013.\left(2013+1\right)}{2}\) + 1
= 0 - 2027091 + 1
= (-2027091) + 1
= -2027090

a) C = 1.2 + 3.4 + 4.5 +...+ 99.100
\(\Rightarrow\) C = 1.2+2.3+3.4+4.5+...+99.100
\(\Rightarrow\)3C = 1.2.3+2.3.3+3.4.3+4.5.3+...+99.100.3
\(\Rightarrow\)3C = 1.2.3+2.3.(4-1)+3.4.(5-2)+4.5.(6-3)+...+99.100.(101-98)
\(\Rightarrow\)3C = 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+...+99.100.101-98.99.100
\(\Rightarrow\)3C = 1.2.3-1.2.3+2.3.4-2.3.4+3.4.5-3.4.5+4.5.6-4.5.6+...+99.100.101
\(\Rightarrow\)3C = 99.100.101
\(\Rightarrow C=33.100.101\)
\(\Rightarrow C=333300\)
b) D = 2 + 4 + 6 + 333 300
\(\Rightarrow\)D = 4 + 16 + 36 + 333 300
\(\Rightarrow\)D = 20 + 36 + 333 300
\(\Rightarrow\)D = 56 + 333 300
\(\Rightarrow\)D = 333 356
a, C = 1.2 + 2.3 + 3.4 + ... + 99.100
3C = 1.2.3 + 2.3.3 + 3.4.3 + .... + 99.100.3
3C = 1.2.3 + 2.3\((4-1)\)+ 3.4\((5-2)+...\)+ 99.100\((101-98)\)
3C = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100
3C = 99.100.101
C = 99.100.101 :3
C = 333300
Câu b tự làm
P/S : Hoq chắc :>

a) 100-(x+21) = 25 b) 55-3x = 59 : 57 c) 43 - 2.(x-21) = 62
x+21 = 100-25 55-3x = 52 64 - 2.(x-21) = 36
x+21 = 75 55-3x = 25 2.(x-21) = 64-36
x = 75-21 3x = 55-25 2.(x-21) = 28
x = 54 3x = 30 x-21 = 28 : 2
x = 30 : 3 x-21 = 14
x = 10 x = 14+21
x = 35
Câu d chưa nghĩ ra,hì hì!
a) 100-(X+21)=25
x+21=25+100
x+21=125
x=125-21
x=104
b) 55-3x=5^9:5^7
55-3x=5^2
55-3x=25
3x=55-25
3x=30
x=30:3
x=10
c) 4^3-2.(x-21)=6^2
4^3-2.(x-21)=36
64-2.(x-21)=36
2.(x-21)=64-36
2.(x-21)=28
x-21=28:2
x-21=14
x=14+21
x=35
Xin lỗi bn mk chỉ giải đc vậy thôi xin thông cảm nha
3.42 + 26 : 24
= 3.16+22
= 3.16+4
= 48+4
=52