Question

Giup minh bai nay nha !^-^

Chung minh rang :

      1/2-1/4+1/8-1/16+1/32-1/64 nho hon 1/3

Ban nao nhanh tay se nhan duoc LIKE!

Answer 1

Đặt \(A=\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}=\frac{1}{2}-\frac{1}{2^2}+\frac{1}{2^3}-\frac{1}{2^4}+\frac{1}{2^5}-\frac{1}{2^6}\)

\(2A=1-\frac{1}{2}+\frac{1}{2^2}-\frac{1}{2^3}+\frac{1}{2^4}-\frac{1}{2^5}\)

\(2A+A=3A=1-\frac{1}{2^6}=\frac{2^6-1}{2^6}< 1\)

\(\Rightarrow3A< 1\Rightarrow A< \frac{1}{3}\)(ĐPCM)