Chứng minh rằng : M = 3^5 + 3^6 + 3^7 + 3^8 + 3^9 + 3^10 chia hết cho 91

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1. Đáp án:

   M = 3^5 + 3^6 + 3^7 + 3^8 + 3^9 + 3^10

   M=3^5.1+3^5.3+3^5.3^2+3^5.3^3+3^5.3^4+3^5.3^5

   M=3^5.(1+3+3^2+3^3+3^4+3^5)

   M=3^5.(1+3+9+27+81+243)

   M=3^5.364

   M=3^5.4.91 chia hết cho 91

   Vậy M chia hết cho 91

   CHO MÌNH XIN HAY NHẤT NHA

   THANK YOU VERY MUCH

    

   Trả lời

2. `M=3^{5}+ 3^{6}+3^{7}+3^{8}+3^{9}+3^{10}`
   `=(3^{5}+3^{7}+3^{9})+(3^{6}+3^{8}+3^{10})`
   `=3^{5}(1+3^{2}+3^{4})+3^{6}(1+5^{2}+3^{4})`
   `=3^{5}.91+3^{6}.91`
   `=91.(3^{5}+3^{6})⋮91`

   Trả lời