a, 55 - [ 49 - ( $2^{3}$ . 17 - $2^{3}$ .14) ] = 55 - [ 49 - ( 8 . 17 - 8 . 14) ] = 55 - { 49 - [ 8 . (17 - 14) ] }
= 55 - [ 49 - ( 8 . 3 ) ] = 55 - ( 49 - 24 ) = 55 - 25 = 30
b, $10^{2}$ - [ 60 : ( $5^{6}$ : $5^{4}$ - 3 . 5 ) ] = 100 - [ 60 : ( $5^{2}$ - 15 ) ]
= 100 - [ 60 : ( 25 - 15 ) ] = 100 - ( 60 : 10) = 100 - 6 = 94
c, 160 : { 17 + [ $3^{2}$ . 5 - ( 14 + $2^{11}$ : $2^{8}$ ) ] } = 160 : { 17 + [ 9 . 5 - ( 14 + $2^{3}$ ) ] }
= 160 : { 17 + [ 9 . 5 - ( 14 + 8 ) ] } = 160 : [ 17 + ( 9 . 5 - 22 ) ] = 160 : [ 17 + ( 45 - 22 ) ]
= 160 : ( 17 + 23 ) = 160 : 40 = 4
d, 798 + 100 : [ 16 - 2 . ( $5^{2}$ - 22) ] = 798 + 100 : [ 16 - 2 . ( 25 - 22) ] = 798 + 100 : ( 16 - 2 . 3 )
= 798 + 100 : ( 16 - 6 ) = 798 + 100 : 10 = 798 + 10 = 808
Bài 2:
a, 2001 - (53 + 1579) - (-53) = 2001 - 53 - 1579 + 53 = 2001 - (53 - 53) - 1579 = 2001 - 1579 = 422
b, (-167) . ( 67 - 34 ) - 67 . ( 34 - 167 ) = (-167) . 67 + 167 . 34 - 67 . 34 + 67 . 167 = 167 . 34 - 67 . 34
= 34 . ( 167-67 ) = 34 . 100 = 3400
c, 1 + (-4) + 2 + (-5) + 3 + (-6) + ... + 17 + (-20)
= [ 1 + (-4) ] + [ 2 + (-5) ] + [ 3 + (-6) ] + ... + [ 17 + (-20) ]
= (-3) + (-3) + (-3) + ... + (-3) + (-3)
= (-3) . 17
= -51
d, 1 + $3^{2}$ + $3^{4}$ + ... + $3^{2018}$
Đặt N = 1 + $3^{2}$ + $3^{4}$ + ... + $3^{2018}$
$3^{2}$ . N = $3^{2}$ + $3^{4}$ + ... + $3^{2018}$ + $3^{2020}$
9 . N - N = $3^{2}$ + $3^{4}$ + ... + $3^{2018}$ + $3^{2020}$ - 1 - $3^{2}$ - $3^{4}$ - ... - $3^{2018}$
8 . N = $3^{2020}$ - 1
N = $\frac{3^{2020} - 1}{8}$
Bài 3:
A = 1 + 4 + $4^{2}$ + $4^{3}$ + $4^{4}$ + $4^{5}$ + $4^{6}$ + $4^{7}$ + $4^{8}$
= ( 1 + 4 + $4^{2}$ ) + $4^{3}$ . ( 1 + 4 + $4^{2}$ ) + $4^{6}$ . ( 1 + 4 + $4^{2}$ )
= 21 + $4^{3}$ . 21 + $4^{6}$ . 21 = 21 . ( 1 + $4^{3}$ + $4^{6}$ ) chia hết cho 21
Vì 21 chia hết cho 3 và 7
⇒ A chia hết cho 3
(xin hay nhất)
Chúc bạn học tốt!!!
