Toán Lớp 6: 1+2+2^2+2^3+2^4+-+2^89 mà chia hết cho 85

Question

Toán Lớp 6:  1+2+2^2+2^3+2^4+....+2^89 mà chia hết cho 85

dinhcongson · Answer

Lời giải và giải thích chi tiết:     -Đặt A = 1+2+2^2+2^3+2^4+......+2^89   => A=(1+2^2)+(2+2^3)+............+(2^87+2^89)   => A=(1+4)+2.(1+4)+............+2^87 . (1+4)   => A=5.(1+2+...............+2^87) vdots 5 (1)   -Ta c&oacute;:  A = 1+2+2^2+2^3+2^4+......+2^89   => A=(1+2^4)+(2+2^5)+...........+(2^85+2^89)   => A=(1+16)+2.(1+16)+..........+2^85 . (1+16)   => A = 17 . (1+2+..........+2^85) vdots 17 (2)   -Từ (1) v&agrave; (2) => A vdots 5 . 17   => A vdots 85 (đpcm)

tongtung · Answer

Đặt A       A=1+2+2^2+2^3+2^4+......................+2^89       A=(1+2+2^2+2^3+2^4+2^5+2^6+2^7)+......................+(2^82+2^83+2^84+2^85+2^86+2^87+2^88+2^89)       A=1.(1+2+2^2+2^3+2^4+2^5+2^6+2^7)+.........................+2^82.(1+2+2^2+2^3+2^4+2^5+2^6+2^7)       A=1.225+.....................+2^82. 225       A=225.(1+.............................+2^82)       V&igrave; 225vdots85       =>Avdots85       Vậy Avdots85