a, Chứng minh rằng A chia hết cho 3
A = 2 + 22 + 23 + .....+ 260
A = ( 2+22 ) + (23 + 24 ) + .....+ (259 + 260 )
A = 2(1+2 ) + 23(1+2) +,...+ 259(1+2)
A = 2.3 + 23.3 + ....+259.3
A = 3(2+23+....+259 ) \(⋮3\)
=> đpcm
chứng minh ằng A chia hết cho 7
A = 2+22 + 23 + .....+ 260
A = ( 2+22 + 23 ) + (24 + 25 + 26) + .... + (258+259+260)
A = 2(1+2 +22 ) +24 (1+2 +22 ) + .... +258(1+2 +22 )
A = 2.7 +24.7 + ....+258.7
A= 7(2+24 ....+258 )\(⋮7\)
=> đpcm
Chứng minh A chia hết cho 15
A = 2 + 22 + 23 + .....+ 260
A = ( 2 + 22 + 23 +24 ) +....+ (257 + 258 + 259 + 260 )
A = 2(1+2+22 + 23 ) + .....+ 257(1+2+22+23)
A = 2.15 + ....+ 257.15
A = 15.(2+...+257) \(⋮15\)
=> đpcm
b,
chứng minh chia hết cho 13
B= 3 + 33 + 35 + + ..........+ 31991
B = (3+33 + 35 ) + (37 + 39 +311 ) + ......+ (31987 + 31989 + 31991 )
B = 3(1+32 +34 ) + 37(1+32 + 34 ) + ....+ 31987(1+32 + 34 )
B = 3.91 + 37.91 + ...+ 31987.91
B = 91(3+37 + ... 31987 )
B = 7.13.(3+37 + ... 31987 ) \(⋮13\)
=> đpcm
chứng minh chia hết cho 41
B = 3+33 + 35 + ...+ 31991
B = (3+33 + 35 + 37 ) + ...(31985 + 31987 + 31989 + 31991 )
B = 3(1+32 + 34 + 36 ) + ...+ 31985(1+32 + 34 + 36)
B = 3. 820 + ...+ 31985.820
B = 820(3+...+31985)
B = 20.41 (3+...+31985) \(⋮41\)
=> đpcm
