B=1+3^1+3^2+3^3+3^4+…+3^2019 chia cho 13 ;40 dư là ?

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1. Đáp án + Giải thích các bước giải:

   `B=1+3^{1}+3^{2}+3^{3}+3^{4}+….+3^{2019}`

   `=(1+3^{1}+3^{2})+(3^{3}+3^{4}+3^{5})+….+(3^{2017}+3^{2018}+3^{2019})`

   `=(1+3+3^{2})+3^{3}(1+3+3^{2})+….+3^{2017}(1+3+3^{2})`

   `=13+3^{3}.13+….+3^{2017}.13`

   `=13(1+3^{3}+…+3^{2017})` `\vdots 13`

   `————–`

   `B=1+3^{1}+3^{2}+3^{3}+3^{4}+….+3^{2019}`

   `=(1+3^{1}+3^{2}+3^{3})+….+(3^{2016}+3^{2017}+3^{2018}+3^{2019})`

   `=(1+3+3^{2}+3^{3})+….+3^{2016}(1+3+3^{2}+3^{3})`

   `=40+…+3^{2016}.40`

   `=40.(1+…+3^{2016})` `\vdots 40`

   Vậy số dư khi chia `B` cho `13` là : `0`

          số dư khi chia `B` cho `40` là : `0`

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2. Đáp án + Giải thích các bước giải:

   `B=1+3^1+3^2+3^3+3^4+3^5+…+3^2017+3^2018+3^2019`
   

   `=>B=(1+3^1+3^2)+(3^3+3^4+3^5)+…+(3^2017+3^2018+3^2019)`
   

   `=>B=1(1+3^1+3^2)+3^3(1+3^1+3^2)+…+3^2017(1+3^1+3^2)`
   

   `=>B=1. 13+3^3. 13+…+3^2017. 13`
   

   `=>B=13(1+3^3+…+3^2017)\vdots13`
   

   `=>B:13` dư `0`

   `—————–`

   `B=1+3^1+3^2+3^3+3^4+3^5+3^6+3^7+…+3^2016+3^2017+3^2018+3^2019`
   

   `=>B=(1+3^1+3^2+3^3)+(3^4+3^5+3^6+3^7)+…+(3^2016+3^2017+3^2018+3^2019)` 
   

   `=>B=1(1+3^1+3^2+3^3)+3^4(1+3^1+3^2+3^3)+…+3^2016(1+3^1+3^2+3^3)` 
   

   `=>B=1.40+3^4. 40+…+3^2016. 40` 
   

   `=>B=40(1+3^4+…+3^2016)\vdots40`
   

   `=>B:40` dư `0`

    

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