Toán cho A=3+3^2+…+3^100 CHỨNG MINH RẰNG A chia hết cho 8 02/12/2021 By Vivian cho A=3+3^2+…+3^100 CHỨNG MINH RẰNG A chia hết cho 8
A=3+3^2+…+3^100 A=(3.1+3.3+3^2.3+3^3.3)+…+(3^97.1+3^97.3+3^97.3^2+3^97.3^3) A=3.(1+3+3^2+3^3)+…+3^97.(1+3+3^2+3^3) A=3.40+…+3^97.40 A=40.(3+….+3^97) CHIA HẾT CHO 8(VÌ 40 CHIA HẾT CHO 8) ⇒A CHIA HẾT CHO 8 ⇒ĐPCM Trả lời
Đáp án: `A=3+3^2+…+3^100` `=(3+3^2+3^3+3^4)+(3^5+3^6+3^7+3^8)+…+(3^97+3^98+3^99+3^100)` `=3(1+3+3^2+3^3)+3^5(1+3+3^2+3^3)+…+3^97(1+3+3^2+3^3)` `=3.40+3^5.40+…+3^97. 40` `=40(3+3^5+…+3^97) vdots 8` Trả lời
A=3+3^2+…+3^100
A=(3.1+3.3+3^2.3+3^3.3)+…+(3^97.1+3^97.3+3^97.3^2+3^97.3^3)
A=3.(1+3+3^2+3^3)+…+3^97.(1+3+3^2+3^3)
A=3.40+…+3^97.40
A=40.(3+….+3^97) CHIA HẾT CHO 8(VÌ 40 CHIA HẾT CHO 8)
⇒A CHIA HẾT CHO 8
⇒ĐPCM
Đáp án:
`A=3+3^2+…+3^100`
`=(3+3^2+3^3+3^4)+(3^5+3^6+3^7+3^8)+…+(3^97+3^98+3^99+3^100)`
`=3(1+3+3^2+3^3)+3^5(1+3+3^2+3^3)+…+3^97(1+3+3^2+3^3)`
`=3.40+3^5.40+…+3^97. 40`
`=40(3+3^5+…+3^97) vdots 8`