Question

Tính nhanh :

A=1+2+4+8+16+...+8192

 

Answer 1

A = 1 + 2 + 4 + 8 + 16 + ... + 8192

A = 2⁰ + 2¹ + 2² + 2³ + 2⁴ + ... + 2¹³

2A = 2¹ + 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁴

2A - A = (2¹ + 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁴) - (2⁰ + 2¹ + 2² + 2³ + 2⁴ + ... + 2¹³)

A = 2¹⁴ - 2⁰

A = 16384 - 1

A = 16383

Answer 2

Ta có: A = 1 + 2 + 4 + 8 + 16 + ....... + 8192

=> 2A = 2 + 4 + 8 + 16 + ....... + 8192 + 16384

=> 2A - A = 16384 - 1

=> A = 16383