Question

So sánh   \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{100}}\)với 1

Answer 1

Đặt A = 1/2 + 1/2^2 + ... +1/2^100

2A  = \(1+\frac{1}{2}+\frac{1}{2^2}+..+\frac{1}{2^{99}}\)

2A - A = \(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{99}}-\frac{1}{2}-\frac{1}{2^2}-..-\frac{1}{2^{99}}-\frac{1}{2^{100}}\)

A = \(1-\frac{1}{2^{100}}

Answer 2

Đặt A = \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{100}}\)

2A = \(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{99}}\)

A = 2A - A = \(1-\frac{1}{2^{100}}