cho A = $1^{3}$+$2^{3}$+ $3^{3}$+…..+ $10^{3}$ Chứng minh rằng: a) A chia hết cho 11 b) A chia hết cho 5

Question

cho A = $1^{3}$+$2^{3}$+ $3^{3}$+…..+ $10^{3}$
Chứng minh rằng: a) A chia hết cho 11
b) A chia hết cho 5

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Madeline 5 tháng 2021-07-10T19:05:04+00:00 1 Answers 10 views 0

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    2021-07-10T19:06:10+00:00

    Ta có:

    $A = 1^3 + 2^3 + 3^3 +\dots + 10^3$

    $\to A = (1 + 2 + 3 +\dots + 10)^2$

    $\to A = \left[\dfrac{10.(10+1)}{2}\right]^2$

    $\to A = (5.11)^2$

    $\to \begin{cases}A \quad \vdots\quad 11\\A \quad \vdots \quad 5\end{cases}$

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