Toán Lớp 6: Cho A=2+2²+2³+…+2⁶⁰.Chứng tỏ rằng A chia hết cho 3,chia hết cho 7,chia hết cho 5
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Toán Lớp 6: Cho A=2+2²+2³+…+2⁶⁰.Chứng tỏ rằng A chia hết cho 3,chia hết cho 7,chia hết cho 5
Comments ( 2 )
A=(2+2^2)+(2^3+2^4)+…………+(2^59+2^60)
A=2.(1+2)+2^3.(1+2)+……………..+2^59.(1+2)
A=2.3+2^3. 3+……………..+2^59. 3
A=3.(2+2^3+…………….+2^59)
Vì 3vdots3
=>Avdots3
A=2+2^2+2^3+………..+2^60
A=(2+2^2+2^3)+…………….+(2^58+2^59+2^60)
A=2.(1+2+2^2)+………………..+2^58.(1+2+2^2)
A=2.7+………………….+2^58. 7
A=7.(2+………………+2^58)
Vì 7vdots7
=>Avdots7
A=2+2^2+2^3+………..+2^60
A=(2+2^2+2^3+2^4)+……………..+(2^57+2^58+2^59+2^60)
A=1.(1+2+2^2+2^3)+……………….+2^57.(1+2+2^2+2^3)
A=1.15+…………………+2^57. 15
A=15.(1+………………..+2^57)
Vì 15vdots5
=>Avdots5
A = 2(1+2) + … + 2 mũ 59 (1+2)
A =2.3 +…+ 2 mũ 59.3
Vậy A chia hết cho 3 , chia hết cho 5 và chia hết cho 7.