\(A=1+2+2^2+2^3+...+2^{99}\)
\(=\left(1+2\right)+2^2\left(1+2\right)+...+2^{98}\left(1+2\right)\)
\(=3\left(1+2^2+...+2^{98}\right)⋮3\)
\(A=1+2+2^2+2^3+2^4+...+2^{95}+2^{96}+2^{97}+2^{98}+2^{99}\)\(A=\left(1+2+2^2+2^3+2^4\right)+2^5\left(1+2+2^2+2^3+2^4\right)+...+2^{95}\left(1+2+2^2+2^3+2^4\right)\)
\(=31\left(1+2^5+....+2^{95}\right)⋮31\)
\(A=1+2+2^2+2^3+...+2^{96}+2^{97}+2^{98}+2^{99}\)
\(=\left(1+2+2^2+2^3\right)+...+2^{96}\left(1+2+2^2+2^3\right)\)
\(=15\left(1+...+2^{96}\right)⋮15\)
\(A=1+2+2^2+....+2^{99}\)
\(A=\left(1+2\right)+\left(2^2+2^3\right)+...+\left(2^{98}+2^{99}\right)\)
\(A=3+2^2\cdot3+...+2^{98}\cdot3\)
\(A=3\cdot\left(1+2^2+...+2^{98}\right)\)
Vậy: A ⋮ 3
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\(A=1+2+2^2+...+2^{99}\)
\(A=\left(1+2+2^2+2^3\right)+\left(2^4+2^5+2^6+2^7\right)+...+\left(2^{96}+2^{97}+2^{98}+2^{99}\right)\)
\(A=15+2^4\cdot15+...+2^{96}\cdot15\)
\(A=15\cdot\left(1+2^4+...+2^{96}\right)\)
Vậy: A ⋮ 15
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\(A=1+2+2^2+...+2^{99}\)
\(A=\left(1+2+2^2+2^3+2^4\right)+...+\left(2^{95}+2^{96}+2^{97}+2^{98}+2^{99}\right)\)
\(A=31+2^5\cdot31+...+32\cdot2^{95}\)
\(A=31\cdot\left(1+2^5+...+2^{95}\right)\)
Vậy A ⋮ 31
