Question

Chứng minh rằng : A = 2 + 2² + 2³ + 2⁴ + .... + 2⁵⁹ + 2⁶⁰  chia het cho 3

Answer 1

A=2+2^2+2^3+...+2^60

A=(2+2^2)+(2^3+2^4)+(2^5+2^6)+...+(2^59+2^60)

A=2(1+2)+2^3(1+2)+2^5(1+2)+...+2^59(1+2)

A=2.3+2^3.3+2^5.3+...+2^59.3

A=3(2+2^3+2^5+...+2^59)

=>A chia hết cho 3

tick nhé mình đầu tiên

Answer 2

A = ( 2 + 2² ) + ( 2³ + 2⁴ ) + ... + ( 2⁵⁹ + 2⁶⁰ )

A = 2 . ( 1+2 ) + 2³ . (1+2) + ... + 2⁵⁹ . (1+2)

A = (2.3 + 2³.3 + ... + 2⁵⁹).3

A = (2+2³+...+2⁵⁹) . 3

=>A chia hết cho 3(ĐPCM)

Answer 3

\(A=2+2^2+2^3+....+2^{60}\)

    \(=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{59}+2^{60}\right)\)

    \(=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{59}\left(1+2\right)\)

    \(=2.3+2^3.3+...+2^{59}.3\)

    \(=3\left(2+2^3+...+2^{59}\right)\)chia hết cho 3