A = (8.3³)⁵.49.7¹³ = (2³.3³)⁵.7².7¹³ = (6³)⁵.7¹⁵ = 6¹⁵.7¹⁵ = 42¹⁵ chia hết cho 42

Chọn

Giải ra đầy đủ nhá

Bài 1:

\(a,A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{2009}+2^{2010}\right)\\ A=\left(1+2\right)\left(2+2^3+...+2^{2009}\right)=3\left(2+...+2^{2009}\right)⋮3\\ A=\left(2+2^2+2^3\right)+...+\left(2^{2008}+2^{2009}+2^{2010}\right)\\ A=\left(1+2+2^2\right)\left(2+...+2^{2008}\right)=7\left(2+...+2^{2008}\right)⋮7\)

\(b,\left(\text{sửa lại đề}\right)B=\left(3+3^2\right)+\left(3^3+3^4\right)+...+\left(3^{2009}+3^{2010}\right)\\ B=\left(1+3\right)\left(3+3^3+...+3^{2009}\right)=4\left(3+3^3+...+3^{2009}\right)⋮4\\ B=\left(3+3^2+3^3\right)+...+\left(3^{2008}+3^{2009}+3^{2010}\right)\\ B=\left(1+3+3^2\right)\left(3+...+3^{2008}\right)=13\left(3+...+3^{2008}\right)⋮13\)

Bài 2:

\(a,\Rightarrow2A=2+2^2+...+2^{2012}\\ \Rightarrow2A-A=2+2^2+...+2^{2012}-1-2-2^2-...-2^{2011}\\ \Rightarrow A=2^{2012}-1>2^{2011}-1=B\\ b,A=\left(2020-1\right)\left(2020+1\right)=2020^2-2020+2020-1=2020^2-1< B\)

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\(A=\left(8.3^3\right)^5.49.7^{13}\)

\(\Rightarrow A=\left(2^3.3^3\right)^5.7^2.7^{13}\)

\(\Rightarrow A=\left[\left(2.3\right)^3\right]^5.7^{15}\)

\(\Rightarrow A=\left(6^3\right)^5.7^{15}\)

\(\Rightarrow A=6^{15}.7^{15}=\left(7.6\right)^{15}=42^{15}⋮42\)

cho mik hỏi câu này nữa   a= 2+2 mũ 3 + 2 mũ 5 +.....+2 mũ 51