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a: Ta có: \(A=2+2^2+2^3+2^4+...+2^{100}\)
\(=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{99}\left(1+2\right)\)
\(=3\cdot\left(2+2^3+...+2^{99}\right)⋮3\)
b: Ta có: \(B=4+4^2+4^3+...+4^{2022}\)
\(=4\left(1+4\right)+4^3\left(1+4\right)+...+4^{2021}\left(1+4\right)\)
\(=5\cdot\left(4+4^3+...+4^{2021}\right)⋮5\)
\(A=2^2+2^4+2^6+...+2^{210}\)
=2^2+2^4+2^6+...+2^206+2^208+2^210
\(=2^2\left(1+2^2+2^4\right)+...+2^{206}\left(1+2^2+2^4\right)\)
\(=21\left(2^2+2^8+...+2^{206}\right)⋮21\)
\(A=47.36+64.47+15\)
\(A=47.\left(36+64\right)+15\)
\(A=47.100+15\)
\(A=4700+15\)
\(A=4715\)
\(B=27+35+65+73+75\)
\(B=\left(27+73\right)+\left(35+65\right)+75\)
\(B=100+100+75\)
\(B=275\)
\(C=37+37.15+84.37\)
\(C=37.\left(1+15+84\right)\)
\(C=37.100\)
\(C=3700\)
\(D=\frac{1}{20.21}+\frac{1}{21.22}+\frac{1}{22.23}+\frac{1}{23.24}\)
\(D=\frac{1}{20}-\frac{1}{21}+\frac{1}{21}-\frac{1}{22}+\frac{1}{22}-\frac{1}{23}+\frac{1}{23}-\frac{1}{24}\)
\(D=\frac{1}{20}-\frac{1}{24}\)
\(D=\frac{24}{480}-\frac{20}{480}\)
\(D=\frac{4}{480}=\frac{1}{120}\)
\(E=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(E=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(E=1-\frac{1}{50}\)
\(E=\frac{49}{50}\)
a: \(2^3-5^3:5^2+12\cdot2^2\)
\(=8-5+48\)
\(=51\)
b: \(5\cdot\left[\left(85-35:7\right):8+90\right]-5\)
\(=5\cdot\left[10+90\right]-5\)
=495
A = 47 x 36 + 64 x 47 + 15
A= 47 x ( 64 + 36 ) + 15 = 47 x 100 + 15 = 4700 + 15 = 4715
vậy A= 4715
B= 27+35 + 65 + 73+ 75
B= (27+ 73) + ( 35 + 65) +75
B= 100 +100 +75 = 275
vậy B= 275
C= 37 +37 x 15 +37 x 84
C= 37 x ( 1+15 +84 )= 37 x 100 = 3700
vậy C= 3700
D = 1/20x21 + 1/21x22 + 1/22x23 + 1/23x24
D= 1/20 - 1/21 + 1/21 - 1/22 + 1/22 - 1/23 + 1/23 - 1/24
D= 1/20 -1/24 = 1/120 vậy D= 1/120
E= 1/1x2 + 1/2x3 + ...... + 1/49x50
E= 1/1 - 1/2 + 1/2 - 1/3 +...... + 1/49 - 1/50
E = 1 - 1/50 = 49/50
vậy E= 49/50
CHÚC HOK TOT
\(\left(\times:23+45\right)\cdot37-22=2^4\cdot105\)
\(\Rightarrow\times\cdot\frac{37}{23}+1665-22=16\cdot105\)
\(\Rightarrow\times\cdot\frac{37}{23}+1643=1680\)
\(\Rightarrow\times\cdot\frac{37}{23}=1680-1643=37\)
\(\Rightarrow\times=37:\frac{37}{23}=23\)
a: \(3^8:3^4+2^2\cdot2^3\)
=81+32
=123
b: \(3\cdot4^2-2\cdot3^2\)
\(=48-18\)
=30
a, 38: 34+ 22. 23
= 38-4 + 22+3
= 34 + 25
= 81 + 32
= 113
b, 3 . 42- 2 . 32
= 3 . 16 - 2 . 9
= 48 - 18
= 30
c, 84 : 4 + 39: 37+ 50
= 84 : 4 + 32 + 1
= 84 : 4 + 9 + 1
= 21 + 9 + 1
= 31
d, 295 - ( 31 - 22 . 5)2
= 295 - ( 31 - 4 . 5 )2
= 295 - ( 31 - 20 )2
= 295 - 112
= 295 - 121
= 174
e, 500 - {5[409 - (23 . 3 - 21)2 ] + 103 } : 15
= 500 - {5[409 - (8 . 3 - 21)2 ] + 103 } : 15
= 500 - {5[409 - (24 - 21)2 ] + 103 } : 15
= 500 - {5[409 - 32 ]+ 103 } : 15
= 500 - {5[409 - 9 ]+ 103 } : 15
= 500 - {5 . 400 + 1000 } : 15
= 500 - {2000 + 1000} : 15
= 500 - 3000 : 15
= 500 - 200
= 300
g, 53 . 2 - 100 : 4 + 23 . 5
= 125 . 2 - 100 : 4 + 8 . 5
= 250 - 25 + 40
= 225 + 40
= 265
h, 205 - [1200 - (42 - 2 . 3)3 ] : 40
= 205 - [ 1200 - ( 16 - 2 . 3 )3 : 40
= 205 - [ 1200 - ( 16 - 6 )3 ] : 40
= 205 - [ 1200 - 103 ] : 40
= 205 - [ 1200 - 1000 ] : 40
= 205 - 200 : 40
= 205 - 5
= 200
Đây nha bạn!!!
a)\(\dfrac{726486}{1333}\)
b)=(21+29)+(28+22)+(27+23)+(26+24)+25
=50.4+25
=200+25
=225
c)
= 23(39+68-7)
=23.100=2300
d)
={2011+[45-(-25)]:4}:2022
=(2011+70:4):2022
=(2011+17,5):2022
=2028,5:2022
=\(\dfrac{4057}{4044}\)