a) C = 1 + 3 + 32 + 33 + ... + 311
C = 30 + 3 + 32 + 33 + ... + 311
C = ( 30 + 3 + 32 ) + ( 33 + 34 + 35 ) + ... + ( 39 + 310 + 311 )
C = ( 30 + 3 + 32 ) + 33 . ( 30 + 3 + 32 ) + ... + 39 . ( 30 + 3 + 32 )
C = 13 + 33 . 13 + ... + 39 . 13
C = 13 . ( 1 + 33 + ... + 39 ) \(⋮\) 13 ( đpcm )
b) C = 1 + 3 + 32 + 33 + ... + 311
C = 30 + 3 + 32 + 33 + ... + 311
C = ( 30 + 3 + 32 + 33 ) + ( 34 + 35 + 36 + 37 ) + ( 38 + 39 + 310 + 311 )
C = ( 30 + 3 + 32 + 33 ) + 34 . ( 30 + 3 + 32 + 33 ) + 38 . ( 30 + 3 + 32 + 33 )
C = 40 + 34 . 40 + 38 . 40
C = 40 . ( 1 + 34 + 38 ) \(⋮\) 40 ( đpcm )
c) A = 4 + 42 + 43 + ... + 423 + 424
A = ( 4 + 42 ) + ( 43 + 44 ) + ... + ( 423 + 424 )
A = ( 4 + 42 ) + 42 . ( 4 + 42 ) + ... + 422 . ( 4 + 42 )
A = 20 + 42 . 20 + ... + 422 . 20
A = 20 . ( 1 + 42 + ... + 422 ) \(⋮\) 20 ( đpcm )
d) A = 4 + 42 + 43 + ...+ 423 + 424
A = ( 4 + 42 + 43 ) + ( 44 + 45 + 46 ) + .... + ( 422 + 423 + 424 )
A = ( 4 + 42 + 43 ) + 43 . ( 4 + 42 + 43 ) + ... + 421 . ( 4 + 42 + 43 )
A = 84 + 43 . 84 + ... + 421 . 84
A = 84 . ( 1 + 43 + ... + 421 )
Vì 81 \(⋮\) 9
=> A = 84 . ( 1 +43 + ... + 421 ) \(⋮\) 21 ( đpcm )
e) A = 4 + 42 + 43 + ... + 423 + 424
A = ( 4 + 42 + 43 + 44 + 45 + 46 ) + ... + ( 417 + 418 + 419 + 421 + 422 + 423 + 424 )
A = ( 4 + 42 + 43 + 44 + 45 + 46 ) + ...+ 416 . ( 4 + 42 + 43 + 44 + 45 + 46 )
A = 5460 + ... + 416 . 5460
A = 5460 . ( 1 + ... + 416 )
Vì 5460 \(⋮\) 420
=> A = 5460 . ( 1 + ... + 416 ) \(⋮\) 420 ( đpcm )
Giải:
*A = 4 + 42 + 43 + ... + 423 + 424
A = (4 + 42) + (43 + 44) + ... + (423 + 424)
A = 1 . (4 + 42) + 42 . (4 + 42) + ... + 422 . (4 + 42)
A = 1 . 20 + 42 . 20 + ... + 422 . 20
A = 20 . (1 + 42 + ... + 422)
Vì 20 \(⋮\)20 nên suy ra 20 . (1 + 42 + ... + 422) \(⋮\)20
=> A \(⋮\)20
Vậy A \(⋮\)20
*A = 4 + 42 + 43 + ... + 423 + 424
A = (4 + 42 + 43) + (44 + 45 + 46) + ... + (422 + 423 + 424)
A = 4 . (1 + 4 + 42) + 44 . (1 + 4 + 42) + ... + 422 . (1 + 4 + 42)
A = 4 . 21 + 44 . 21 + ... + 422 . 21
A = 21 . (4 + 44 + ... + 422)
Vì 21\(⋮\)21 nên suy ra 21 . (4 + 44 + ... + 422) \(⋮\)21
=> A \(⋮\)21
Vậy A \(⋮\)21
*A = 4 + 42 + 43 + ... + 423 + 424
A = (4 + 42 + 43 + 44 + 45 + 46) + (47 + 48 + 49 + 410 + 411 + 412) + ... + (419 + 420 + 421 + 422 + 423 + 424)
A = 1 . (4 + 42 + 43 + 44 + 45 + 46) + 46 . (4 + 42 + 43 + 44 + 45 + 46) + ... + 418 . (4 + 42 + 43 + 44 + 45 + 46)
A = 1 . 5460 + 46 . 5460 + ... + 418 . 5460
A = 5460 . (1 + 46 + ... + 418)
Vì 5460 \(⋮\)420 nên suy ra 5460 . (1 + 46 + ... + 418) \(⋮\)420
=> A \(⋮\)420
Vậy A \(⋮\)420.
Chúc bạn học tốt!
Giải:
*C = 1 + 3 + 32 + 33 + ... + 311
C = (1 + 3 + 32 ) + (33 + 34 + 35) + ... + (39 + 310 + 311)
C = 1. (1 + 3 + 32) + 33 . (1 + 3 + 32) + ... + 39 . (1 + 3 + 32)
C = 1 . 13 + 33 . 13 + ... + 39 . 13
C = 13 . (1 + 33 + ... + 39)
Vì 13 \(⋮\)13 nên suy ra 13 . (1 + 33 + ... + 39) \(⋮\)13
=> C \(⋮\)13.
Vậy C \(⋮\)13.
*C = 1 + 3 + 32 + 33 + ... + 311
C = (1 + 3 + 32 + 33) + (34 + 35 + 36 + 37) + (38 + 39 + 310 + 311)
C = 1. (1 + 3 + 32 + 33) + 34 . (1 + 3 + 32 + 33) + 38 . (1 + 3 + 32 + 33)
C = 1 . 40 + 34 . 40 + 38 . 40
C = 40 . (1 + 34 + 38)
Vì 40 \(⋮\)40 nên suy ra 40 . (1 + 34 + 38) \(⋮\)40
=> C \(⋮\)40
Vậy C \(⋮\)40
Chúc bạn học tốt!
