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215 + 43 - 15 - 23
= (215 - 15) + (43 - 23)
= 200 + 20
= 220
2022 - (122 + 2022) + (122 - 325)
= 2022 - 122 - 2022 + 122 - 325
= (2022 - 2022) - (122 - 122) - 325
= 0 - 0 - 325
= - 325
12.(-137) + 12.136
= 12.( -137 + 136)
= 12.(-1)
= - 12
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231 - ( x - 6 ) = 1339 / 12
( x - 6 ) = 231 - 1339/12
( x - 6 ) = 1373/12
x = 1373/12 + 6
x = 1445/12
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286 - { 122 + 77 - ( 12 + 21 ) }
=286 - { 122 + 77 - 33 }
=286 - {199-33}
=286 - 166=120
286 - { 122+77- (12 + 21) }
=286 - {122 + 77 - 33}
= 286 - 166
= 120
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Đáp án cần chọn là: D
M = 1 + 1 2 + 1 2 2 + 1 2 3 + ... + 1 2 99 + 2 2 100 2 M = 2. 1 + 1 2 + 1 2 2 + 1 2 3 + ... + 1 2 99 + 2 2 100 = 2 + 1 + 1 2 + 1 2 2 + 1 2 3 + ... + 1 2 99
Ta có :
M = 2 M − M = ( 2 + 1 + 1 2 + 1 2 2 + 1 2 3 + ... + 1 2 99 ) − ( 1 + 1 2 + 1 2 2 + 1 2 3 + ... + 1 2 99 + 2 2 100 ) M = 2 M − M = 2 + 1 + 1 2 + 1 2 2 + 1 2 3 + ... + 1 2 98 + 1 2 99 − 1 + 1 2 + 1 2 2 + 1 2 3 + ... + 1 2 99 + 1 2 100 = 2 − 1 2 100 = 2 101 − 1 2 100
![](https://rs.olm.vn/images/avt/0.png?1311)
A = 1 12 + 1 13 + ... + 1 22 > 1 22 + 1 22 + ... + 1 22 ⏟ 11 s = 11 22 = 1 2
![](https://rs.olm.vn/images/avt/0.png?1311)
A = 1 12 + 1 13 + 1 14 + ... + 1 22 > 1 22 + 1 22 + ... 1 22 ⏟ 11 s = 11 22 = 1 2 .
![](https://rs.olm.vn/images/avt/0.png?1311)
A = 1 12 + 1 13 + 1 14 + ... + 1 22 > 1 2 ⇔ 1 12 + 1 13 + 1 14 + ... + 1 22 > 11 22 ⇔ 1 12 − 1 22 + 1 13 − 1 22 + 1 14 − 1 22 + ... + 1 22 − 1 22 > 0
Vì 1 12 > 0 , 1 13 > 0 , ... , 1 21 > 1 22 nên 1 12 − 1 22 > 0 , 1 13 − 1 22 > 0 , ... , 1 21 − 1 22 > 0 , 1 22 − 1 22 = 0
Suy ra A > 1 2