a/ \(A=2+2^2+2^3+-.+2^{60}\)
\(=\left(2+2^2\right)+\left(2^3+2^4\right)+-...+\left(2^{59}+2^{60}\right)\)
\(=2\left(1+2\right)+2^3\left(1+2\right)+-+2^{59}\left(1+2\right)\)
\(=2.3+2^3.3+-..+2^{59}.3\)
\(=3\left(2+2^3+-+2^{59}\right)⋮3\left(đpcm\right)\)
b/Ta có :
\(A=2+2^2+2^3+-.+2^{60}\)
\(=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{58}+2^{59}+2^{60}\right)\)
\(=2\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+-..+2^{58}\left(1+2+2^2\right)\)
\(=2.7+2^3.7+-..+2^{58}.7\)
\(=7\left(2+2^3+-.+2^{58}\right)⋮7\left(đpcm\right)\)
c/ \(A=2+2^2+2^3+-+2^{60}\)
\(=\left(2+2^2+2^3+2^4\right)+\left(2^5+2^6+2^7+2^8\right)+-+\left(2^{57}+2^{58}+2^{59}+2^{60}\right)\)
\(=2\left(1+2+2^2+2^3\right)+2^5\left(1+2+2^2+2^3\right)+-+2^{57}\left(1+2+2^2+2^3\right)\)
\(=2.15+2^5.15+-..+2^{57}.15\)
\(=15\left(2+2^5+-..+2^{57}\right)⋮15\left(đpcm\right)\)
