Question

Bài toán 10  Tính nhanh tổng sau.  A = 1 +2 +4 +8 +16 +....8192

Answer 1

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

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

2A=21+22+23+24+....+2142A=21+22+23+24+....+214

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

⇒A=214−1=16383

Answer 2

Giải :

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

=> A = 2⁰ + 2¹ + 2² + 2³ + ... + 2¹³

=> 2A = 2¹ + 2² + 2³ + 2⁴ + ... + 2¹⁴

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

=> A = 2¹⁴ - 2⁰

=> A = 16 384 - 1 = 16 383