Toán Lớp 6: Chứng minh S= 1+2+2^2+2^3+2^4+2^5+…+2^2018+2^2019 chia hết cho 3.
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Toán Lớp 6: Chứng minh S= 1+2+2^2+2^3+2^4+2^5+…+2^2018+2^2019 chia hết cho 3.
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S = 1 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + … + 2^2018 + 2^2019
⇒ S = (1 + 2) + (2^2 + 2^3) + (2^4 + 2^5) + … + (2^2018 + 2^2019)
⇒ S = (1 +2) + 2^2(1 + 2) + 2^4(1 + 2) + … + 2^2018(1 + 2)
⇒ S = 1 . 3 + 2^2 . 3 + 2^4 . 3 + … + 2^2018 . 3
⇒ S = (1 + 2^2 + 2^4 + … + 2^2018) . 3
Mà 3 vdots 3 ⇒ S vdots 3
giải thích các bước:
S= 1+2+2^2+2^3+2^4+2^5+…+2^2018+2^2019
S= (1+2)+(2^2+2^3)+(2^4+2^5)+…+(2^2018+2^2019)
S=3+2^2 .(1+2)+2^4 .(1+2)+……+2^2018 .(1+2)
S=3+2^2.3+2^4.3+……+ 2^2018 .3
S=3.(1+2^2+2^4+…….+2^2018) chia hết cho 3
⇒ S chia hết cho 3