cứu mik vớiiiiiiiiiiiiiiiiiiiiiiii cho tổng A=2+2^2+2^3+….+2^20 chứng minh rằng a) A chia hết cho 2 b) A chia hết cho 3 c)

cứu mik vớiiiiiiiiiiiiiiiiiiiiiiii
cho tổng A=2+2^2+2^3+….+2^20 chứng minh rằng
a) A chia hết cho 2
b) A chia hết cho 3
c) A chia hết cho 5

1 bình luận về “cứu mik vớiiiiiiiiiiiiiiiiiiiiiiii cho tổng A=2+2^2+2^3+….+2^20 chứng minh rằng a) A chia hết cho 2 b) A chia hết cho 3 c)”

  1. a) A = $\text{2 + $2^{2}$ + $2^{3}$ + $2^{4}$ + … $2^{20}$}$
    A = $\text{2 . (1 + $2^{2}$ + $2^{3}$ + $2^{4}$ + … $2^{19}$)}$
    ⇒ A $\vdots$ 2
    b) A = $\text{2 + $2^{2}$ + $2^{3}$ + $2^{4}$ + … $2^{19}$ + $2^{20}$}$
    A = $\text{(2 + $2^{2}$) + ($2^{3}$ + $2^{4}$) + … ($2^{19}$ + $2^{20}$)}$
    A = $\text{2 . (1 + 2) + $2^{2}$ . (1 + 2) + … $2^{18}$ . (1 + 2)}$
    A = $\text{2 . 3 + $2^{2}$ . 3 + … $2^{18}$ . 3}$
    A = $\text{3 . (2 + $2^{2}$ … $2^{16}$ + $2^{18}$)}$
    ⇒ A $\vdots$ 3
    c) A = $\text{2 + $2^{2}$ + $2^{3}$ + $2^{4}$ + … $2^{17}$ + $2^{18}$ + $2^{19}$ + $2^{20}$}$
    A = $\text{(2 + $2^{3}$) + ($2^{2}$ + $2^{4}$) + … ($2^{17}$ + $2^{19})$ + ($2^{18}$ + $2^{20})$}$
    A = $\text{2 . (1 + $2^{2}$) + $2^{2}$ . (1 + $2^{2}$) + … $2^{17}$ . (1 + $2^{2}$) + $2^{18}$ . (1 + $2^{2}$)}$
    A = $\text{2 . 5 + $2^{2}$ . 5 + … $2^{17}$ . 5 + $2^{18}$ . 5}$
    A = $\text{5 . (2 + $2^{2}$ … $2^{17}$ + $2^{18}$)}$
    ⇒ A $\vdots$ 5
    $\textit{#TranDucQuangNBK}$

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