Question

Cho A = 2 + 2^2 + 2^3 + 2^4 + 2^5 + .... + 2^10

a) Tính A bằng bao nhiêu    b)  Chứng Minh rằng A chia hết cho 3

Answer 1

a) 

A = 2 + 2² + 2³ + ....................... + 2¹⁰

2A =  2² + 2³ + ....................... + 2¹⁰ + 2¹¹

2A - A = (2² + 2³ + ....................... + 2¹⁰ + 2¹¹) - (2 + 2² + 2³ + ....................... + 2¹⁰)

A = 2¹¹ - 2 

A = 2046 

b) 

A = 2 + 2² + 2³ + ....................... + 2¹⁰

A = (2 + 2²) + (2³ + 2⁴) + ................ + (2⁹ + 2¹⁰)

A = 2.(1 + 2) + 2³ .(1 + 2) + .................. + 2⁹.(1 + 2)

A = 2.3 + 2³.3 + ................. + 2⁹.3

A = 3.(2 + 2³ + ..................... + 2⁹)