Question

 a=2^1 +2^2 +...+2^60 

chứng minh rằng achia hết cho 14

 

Answer 1

\(A=2^1+2^2+......+2^{60}\)

\(A=\left(2^1+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+......+\left(2^{58}+2^{59}+2^{60}\right)\)

\(A=14+2^4.\left(2^1+2^2+2^3\right)+........+2^{58}.\left(2^1+2^2+2^3\right)\)

\(A=14+2^4.14+........+2^{58}.14\)

\(A=14.\left(1+2^4+........+2^{58}\right)⋮54\)

Vậy A chia hết cho 14 ( đpcm )