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Bài 10 trang 93 Tài liệu dạy – học toán 6 tập 1

Giải bài tập Cho số tự nhiên
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Đề bài

Cho số tự nhiên \(B = 7 + {7^2} + {7^3} + {7^4} + {7^5} + {7^6} + {7^7} + {7^8}\). Số B có chia hết cho 5 không ? Tại sao ?

Lời giải chi tiết

\(\eqalign{   B &= 7 + {7^2} + {7^3} + {7^4} + {7^5} + {7^6} + {7^7} + {7^8}  \cr   &  = (7 + {7^3}) + ({7^2} + {7^4}) + ({7^5} + {7^7}) + {7^6} + {7^8}  \cr   &  = 7.(1 + {7^2}) + {7^2}(1 + {7^2}) + {7^5}(1 + {7^2}) + {7^6}(1 + {7^2})  \cr   &  = 7.50 + {7^2}.50 + {7^5}.50 + {7^6}.50  \cr   &  = (7 + {7^2} + {7^5} + {7^6}).50 \cr&= 5.(7 + {7^2} + {7^5} + {7^6}).10\; \vdots \;5 \cr} \)Vậy B chia hết cho 5

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