Toán Lớp 6: 3 + 3^2 + 3^3…..+ 3^2022 +3^2023 chứng tỏ chia hết 40 nha
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Toán Lớp 6: 3 + 3^2 + 3^3…..+ 3^2022 +3^2023 chứng tỏ chia hết 40 nha
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3 + 3^2 + 3^3…..+ 3^2022 +3^2023
=3 + 3^2 + 3^3+3^4+…..+3^2020+3^2021+ 3^2022 +3^2023
=(3 + 3^2 + 3^3+3^4)+…..+(3^2020+3^2021+ 3^2022 +3^2023)
=3(1 + 3 + 3^2+3^3)+…..+3^2020(1 + 3 + 3^2+3^3)
=3(1 + 3 + 9+27)+…+3^2020(1 + 3 + 9+27)
=3.40 + … + 3^2020 .40
=40.(3+3^2020) vdots 40
Vậy biểu thức đã cho chi hết cho 40