Toán B=3+3^2+3^3+3^4+3^5+….3^2019 CHỨNG MINH RẰNG b CHIA HẾT CHO 13 15/11/2021 By Adalyn B=3+3^2+3^3+3^4+3^5+….3^2019 CHỨNG MINH RẰNG b CHIA HẾT CHO 13
Đáp án: Ta có : `B=3+3^2+3^3+…+3^(2019)` `B=(3+3^2+3^3)+(3^4+3^5+3^6)+…+(3^(2017)+3^(2018)+3^(2019))` `B=39+39.3^3+39.3^4+…+39.3^(2016)` `B=39.(1+3^3+3^4+…+3^(2016))` Vì `39.(1+3^3+3^4+…+3^(2016)) vdots 13` `=> B vdots 13` Giải thích các bước giải: Trả lời
Ta có: `B=3+3^2+3^3+…+3^(2019)` `B=(3+3^2+3^3)+(3^4+3^5+3^6)+…+(3^(2017)+3^(2018)+3^(2019))` `B=39+39.3^3+39.3^4+…+39.3^(2016)` `B=39.(1+3^3+3^4+…+3^(2016))` Vì 39`vdots`13 (=3) → B`vdots`13 Trả lời
Đáp án:
Ta có :
`B=3+3^2+3^3+…+3^(2019)`
`B=(3+3^2+3^3)+(3^4+3^5+3^6)+…+(3^(2017)+3^(2018)+3^(2019))`
`B=39+39.3^3+39.3^4+…+39.3^(2016)`
`B=39.(1+3^3+3^4+…+3^(2016))`
Vì `39.(1+3^3+3^4+…+3^(2016)) vdots 13`
`=> B vdots 13`
Giải thích các bước giải:
Ta có:
`B=3+3^2+3^3+…+3^(2019)`
`B=(3+3^2+3^3)+(3^4+3^5+3^6)+…+(3^(2017)+3^(2018)+3^(2019))`
`B=39+39.3^3+39.3^4+…+39.3^(2016)`
`B=39.(1+3^3+3^4+…+3^(2016))`
Vì 39`vdots`13 (=3)
→ B`vdots`13