(Mình chỉ biết làm những bài này thôi nha)
Câu 4:
Sửa đề:
\(S=1+5+5^2+5^3+5^4+5^5+...+5^{65}\)
⇔\(S=5^0+5^1+5^2+5^3+5^4+5^5+...+5^{65}\)
⇔\(S=\left(5^0+5^1+5^2\right)+\left(5^3+5^4+5^5\right)+...+\left(5^{63}+5^{64}+5^{65}\right)\)
⇔\(S=5^0\left(1+5+5^2\right)+5^3\left(1+5+5^2\right)+...+5^{63}\left(1+5+5^2\right)\)
⇔\(S=\left(1+5+5^2\right)\left(5^0+5^3+...+5^{63}\right)\)
Vì \(1+5+5^2=31\) ⋮ \(31\)
⇒ \(S\) ⋮ \(31\)
Câu 5:
\(A=1+3+3^2+...+3^{11}\)
⇔\(A=3^0+3^1+3^2+...+3^{11}\)
⇔\(A=\left(3^0+3^1\right)+\left(3^2+3^3\right)+...+\left(3^{10}+3^{11}\right)\)
⇔\(A=3^0\left(1+3\right)+3^2\left(1+3\right)+...+3^{10}\left(1+3\right)\)
⇔\(A=\left(1+3\right)\left(3^0+3^2+...+3^{10}\right)\)
Vì \(1+3=4\) ⋮ \(4\)
⇒ \(A\) ⋮ \(4\)
