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a) (-21) + |-50| + (-29) – |-2016|
= (-21) + 50 + (-29) – 2016
= [(-21) + (-29) + 50] – 2016 = ( -50 +50 ) – 2016
= 0 – 2016 = - 2016 .
b) 36 : 3 2 + 3 2 . 2 3 - 15 0
= 36 : 9 + 9 . 8 – 1 = 4 + 72 – 1 = 76 – 1 = 75
c) ( 5 103 – 5 102 – 5 101 ) : ( 5 99 . 26 – 5 99 )
= ( 5 103 – 5 102 – 5 101 ) : 5 99 . ( 26 – 1 )
= ( 5 103 – 5 102 – 5 101 ) : ( 5 99 . 25 )
= 5 101 ( 5 2 – 5 1 – 5 0 ) : ( 5 99 . 5 2 )
= ( 5 101 . 19 ) : 5 101 = 19
c) ( 5 103 - 5 102 - 5 101 ) : ( 5 99 . 26 - 5 99 )
= ( 5 103 - 5 102 - 5 101 ) : [ 5 99 . ( 26 – 1)]
= ( 5 103 - 5 102 - 5 101 ) : ( 5 99 . 25 )
= 5 101 ( 52 – 51 – 50) : ( 5 99 . 52 )
= ( 5 101 . 19 ) : 5 101 = 19
a, Ta có :
A = 1 + 2 + 2 2 + 2 3 + 2 4 + . . . + 2 99 + 2 100
2A = 2 + 2 2 + 2 3 + 2 4 + . . . + 2 99 + 2 100 + 2 101
A = 2A – A = ( 2 + 2 2 + 2 3 + 2 4 + . . . + 2 99 + 2 100 + 2 101 ) –( 1 + 2 + 2 2 + 2 3 + 2 4 + . . . + 2 99 + 2 100 )
= 2 + 2 2 + 2 3 + 2 4 + . . . + 2 99 + 2 100 + 2 101 – 1 - 2 - 2 2 - 2 3 - 2 4 - . . . - 2 99 - 2 100
= 2 101 - 1
Vậy A = 2 101 - 1
b, Ta có.
B = 5 + 5 3 + 5 5 + . . . + 5 97 + 5 99
5 2 B = 5 2 ( 5 + 5 3 + 5 5 + . . . + 5 97 + 5 99 )
25B = 5 3 + 5 5 + . . . + 5 97 + 5 99 + 5 101
25B – B = ( 5 3 + 5 5 + . . . + 5 97 + 5 99 + 5 101 ) – ( 5 + 5 3 + 5 5 + . . . + 5 97 + 5 99 )
24B = 5 3 + 5 5 + . . . + 5 97 + 5 99 + 5 101 – 5 - 5 3 - 5 5 - . . . - 5 97 - 5 99
24B = 5 101 - 5
B = 5 101 - 5 24 = 5 5 100 - 1 24
Vậy B = 5 5 100 - 1 24
a) 23 + 25 + 27 + 29 + 31 + 33 + 35
= 23 + ( 25 + 35 ) + ( 27 + 33 ) + ( 29 + 31 )
= 23 + 60 + 60 + 60
= 23 + 60 x 3
= 23 + 180
= 203
b) 4 . 36 . 25 . 50
= 4 . 4 .9 . 25 . 25 . 2
= 4 . 25 . 4 . 25 . 9 . 2
= 100 . 100 . 9 . 2
= 10 000 . 18
= 180 000
c) 32 . 125 . 3
= 4 . 8 . 5 . 25 . 3
= 4 . 25 . 8 . 5 . 3
= 100 . 8 . 5 . 3
= 800 . 5 . 3
= 4000 . 3
= 12000
d, 36 . 19 + 36 . 81
= 36 . ( 19 + 81 )
= 36 . 100
= 3600
e, 78 . 31 + 78 . 24 + 78 . 17 + 22 x 72
= 78 . ( 31 + 24 + 17 ) + 22 x 72
= 78 . 72 + 22 . 72
= 72 . ( 78 + 22 )
= 72 . 100
= 7200
A)23+25+27+29+31+33+35
= (33+27)+(25+35)+(29+31)+23
=60+60+60+23
=60x3+23
=180+23
=203
B)4.36.25.50=(36.25).(4.50)
=(4.9.25).(2.2.50)
=(4.25).9 .(2.50).2
=100.9.100.2
=100.(9+2)
=100 .11
=1100
C)32.125.3=(4.8).125.3
=(125.8).(4.3)
=1000.12
=12000
D)36.19.36.81=36.(19+81)
= 36.100
=3600
E)78.31.+78.24+78.17+22x72=78.31+78.24+78.17+ (16+6).72
=78.31+78.24+78.17+78.16
=78.(31+24+17+16)
=78.88
=6864
a) (-21) + | -50 | + (-29) – | -2016 |
= -21 + 50 - 29 -2016
= (-21 - 29 +50 ) -2016
= -2016
b) 36 : 32 + 32 . 23 -150 ( xem lại đề nhé )
c) ( 5103 – 5102 – 5101) : ( 599 . 26 – 599)
= ( 1 - 5101 ) : ( 599 . ( 26 - 1 ) )
= - 5100 : (599 . 25)
= \(-\frac{204}{599}\)