Toán Lớp 6: giúp mình với ạ mình đang cần gấp
Câu 7:(0.5đ): Chứng tỏ rằng :
A= 2+ 2^2+ 2^3 + 2^4 +…+2^100 vừa chia hết cho 31, vừa chia hết cho 5
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Toán Lớp 6: giúp mình với ạ mình đang cần gấp
Câu 7:(0.5đ): Chứng tỏ rằng :
A= 2+ 2^2+ 2^3 + 2^4 +…+2^100 vừa chia hết cho 31, vừa chia hết cho 5
Comments ( 2 )
7)
A=2+2^2+2^3+2^4+……………………….+2^100
A=(2+2^2+2^3+2^4)+……………………….+(2^97+2^98+2^99+2^100)
A=2.(1+2+2^2+2^3)+……………………….+2^97.(1+2+2^2+2^3)
A=2.15+………………………+2^97. 15
A=15.(2+…………………….+2^97)
Vì 15vdots5
=>Avdots5
Vậy Avdots5
A=2+2^2+2^3+2^4+……………………….+2^100
A=(2+2^2+2^3+2^4+2^5)+ …………………………..+(2^96+2^97+2^98+2^99+2^100)
A=2.(1+2+2^2+2^3+2^4)+………………………….+2^96.(1+2+2^2+2^3+2^4)
A=2.31+………………………….+2^96. 31
A=31.(2+…………………….+2^96)
Vì 31vdots31
=>Avdots31
Vậy Avdots31
@Ki ng
A = 2 + 2^2 + 2^3 + 2^4 + … + 2^100
A = ( 2 + 2^2 + 2^3 + 2^4 + 2^5 ) + ( 2^6 + 2^7 + 2^8 + 2^9 + 2^10 ) + … + ( 2^96 + 2^97 + 2^98 + 2^99 + 2^100 )
A = 1( 2 + 2^2 + 2^3 + 2^4 + 2^5 ) + 2^5( 2 + 2^2 + 2^3 + 2^4 + 2^5 ) + … + 2^95( 2 + 2^2 + 2^3 + 2^4 + 2^5 )
A = 1 * 62 + 2^5 * 62 + … + 2^95 * 62
A = ( 1 + 2^5 + 2^95 ) * 62
⇒ A vdots 31
A = 2 + 2^2 + 2^3 + 2^4 + … + 2^100
A = ( 2 + 2^2 + 2^3 + 2^4 ) + ( 2^5 + 2^6 + 2^7 + 2^8 ) + … + ( 2^97 + 2^98 + 2^99 + 2^100 )
A = 1( 2 + 2^2 + 2^3 + 2^4 ) + 2^4( 2 + 2^2 + 2^3 + 2^4 ) + … + 2^96( 2 + 2^2 + 2^3 + 2^4 )
A = 1 * 30 + 2^4 * 30 + … + 2^96 * 30
A = ( 1 + 2^4 + … + 2^96 ) * 30
⇒ A vdots 5