Cho C=2+2^2+2^3+…+2^99+2^100 chứng minh C chia hết cho 15 29/09/2021 Bởi Melody Cho C=2+2^2+2^3+…+2^99+2^100 chứng minh C chia hết cho 15
`C = 2 + 2^2 + 2^3 + … + 2^100` `⇒ C = (2 + 2^2 + 2^3 + 2^4) + … + (2^97 + 2^98 + 2^99 + 2^100)` `⇒ C = 2(1 + 2 + 2^2 + 2^3) + … + 2^97(1 + 2 + 2^2 + 2^3)` `⇒ C = 2. 15 + … + 2^97. 15 ⋮ 15` `⇒ C ⋮ 15` `⇒ đpcm` Bình luận
Đáp án: C=2+2^2+2^3+…+2^99+2^100 C=(2+2^2+2^3+2^4)+…………..+(2^97+2^98+2^99+2^100) C=2.(1+2+4+8)+…………….+2^97.(1+2+4+8) C=2.15+2^5.15+…………+2^97.15 C=15.(2+2^5+……+2^97) chia hết cho 15 =>C chia hết cho 15 XIN HAY NHẤT NHA Bình luận
`C = 2 + 2^2 + 2^3 + … + 2^100`
`⇒ C = (2 + 2^2 + 2^3 + 2^4) + … + (2^97 + 2^98 + 2^99 + 2^100)`
`⇒ C = 2(1 + 2 + 2^2 + 2^3) + … + 2^97(1 + 2 + 2^2 + 2^3)`
`⇒ C = 2. 15 + … + 2^97. 15 ⋮ 15`
`⇒ C ⋮ 15`
`⇒ đpcm`
Đáp án:
C=2+2^2+2^3+…+2^99+2^100
C=(2+2^2+2^3+2^4)+…………..+(2^97+2^98+2^99+2^100)
C=2.(1+2+4+8)+…………….+2^97.(1+2+4+8)
C=2.15+2^5.15+…………+2^97.15
C=15.(2+2^5+……+2^97) chia hết cho 15
=>C chia hết cho 15
XIN HAY NHẤT NHA