Question

cho A = 2 + 2^2 + 2^3 + ........+ 2^60. Chứng minh rằng A chia hết cho 3

Answer 1

A=2+2²+2³+...+2⁶⁰

= ( 2+2²)+(2³+2⁴)+...+(2⁵⁹+2⁶⁰)

= 2. 3 + 2³.3+...+2⁵⁹.3

= 3.( 2+2³+...+2⁵⁹) chia het cho 3

=> A chia het cho 3

Answer 2

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

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

   = 2. 3 + 2³ . 3 + .... + 2⁵⁹ x 3

   = 3(2 + 2³ + .... + 2⁵⁹ ) chia hết cho 3