Question

[Lê Xuân Huy]

1/2+1/4+1/8+1/16+..........................+1/2048

Answer 1

[Nguyen Viet Bac]

Gọi biểu thức trên là A Ta có :

A = \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+......+\frac{1}{2048}\)

=> A : 2 = \(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+....+\frac{1}{2048}+\frac{1}{4096}\)

=> \(\frac{1}{2}\)A = \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+......+\frac{1}{2048}\)- \(\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}-......-\frac{1}{2048}-\frac{1}{4096}\)

=> A : 2 = \(\frac{1}{2}-\frac{1}{4096}\)

=> A : 2 = \(\frac{2047}{4096}\)

=> A = \(\frac{2047.2}{4096}\)

=> A = \(\frac{4094}{4096}\)

Answer 2

[soyeon_Tiểu bàng giải]

Đặt A = 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/2048

2A = 1 + 1/2 + 1/4 + 1/8 + ... + 1/1024

2A - A = (1 + 1/2 + 1/4 + 1/8 + ... + 1/1024) - (1/2 + 1/4 + 1/8 + 1/16 + ... + 1/2048)

A = 1 - 1/2048

A = 2047/2048