Toán Lớp 6: cho A = 2+2^2+2^3+-..+2^60 chứng minh rằng A chia hết cho 3 ,A chia hết cho 7, A chia hết cho 5

Question

Toán Lớp 6:  cho A = 2+2^2+2^3+......+2^60 chứng minh rằng A chia hết cho 3 ,A chia hết cho 7, A chia hết cho 5

thienthanh · Answer

a)ta c&oacute;: A = 2+2^2+2^3+......+2^60            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)   VẬY A$ vdots$3   B)TA C&Oacute;: A = 2+2^2+2^3+......+2^60   A = (2+2^2+2^3)+(2^4+2^5+2^6)+......(2^58+2^59+2^60)   A=2.(1+2+2^2)+2^4.(1+2+2^2)+...+2^58.(1+2+2^2)   A=2.14+2^4.14+...+2^58.14   A=14.(2+2^4+...+2^58)   V&Igrave;  14$ vdots$7$ Rightarrow$A$ vdots$7$   C)TA C&Oacute;: 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=2.(1+2+2^2+2^3)+2^4.(1+2+2^2+2^3)+...+2^58.(1+2+2^2+2^3)   A=2.30+2^4.30+...2^58.30   A=30.(2+2^4+..+2^58)   V&Igrave; 30          $ vdots$5 $ Rightarrow$A$ vdots$5