Question

\(2^1+2^2+2^3+2^4+...+2^{150}=A\)

Chứng minh A ⋮ 3

Answer 1

\(A=2^1+2^2+2^3+2^4+...+2^{150}\)

\(< =>A=\left(2^1+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{149}+2^{150}\right)\)

\(< =>1.6+2^3.\left(2^1+2^2\right)+...+2^{149}.\left(2^1+2^2\right)\)

\(< =>1.6+2^3.6+...+2^{149}.6\)

\(< =>\left(1+2^3+...+2^{149}\right).6\)

\(< =>A⋮6⋮3\)