Câu hỏi của nguyễn trần quỳnh trâm

Question

a)Chứng tỏ: A = 3¹ + 3² + 3³ + … + 3⁶⁰ chia hết cho 13

b)Cho M = 2 + 2² + 2³ + … + 2^...

Nguyễn Hoàng Minh · Accepted Answer

$A=\left(3+3^2+3^3\right)+...+\left(3^{58}+3^{59}+3^{60}\right)\ A=3\left(1+3+3^2\right)+...+3^{58}\left(1+3+3^2\right)\ A=\left(1+3+3^2\right)\left(3+...+3^{58}\right)\ A=13\left(3+...+3^{58}\right)⋮13$

$M=\left(2+2^2+2^3+2^4\right)+...+\left(2^{17}+2^{18}+2^{19}+2^{20}\right)\ M=\left(2+2^2+2^3+2^4\right)+...+2^{16}\left(2+2^2+2^3+2^4\right)\ M=\left(2+2^2+2^3+2^4\right)\left(1+...+2^{16}\right)\ M=30\left(1+...+2^{16}\right)⋮5$

Câu trả lời:

$A=\left(3+3^2+3^3\right)+...+\left(3^{58}+3^{59}+3^{60}\right)\ A=3\left(1+3+3^2\right)+...+3^{58}\left(1+3+3^2\right)\ A=\left(1+3+3^2\right)\left(3+...+3^{58}\right)\ A=13\left(3+...+3^{58}\right)⋮13$

$M=\left(2+2^2+2^3+2^4\right)+...+\left(2^{17}+2^{18}+2^{19}+2^{20}\right)\ M=\left(2+2^2+2^3+2^4\right)+...+2^{16}\left(2+2^2+2^3+2^4\right)\ M=\left(2+2^2+2^3+2^4\right)\left(1+...+2^{16}\right)\ M=30\left(1+...+2^{16}\right)⋮5$

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