Question

So sánh

\(\dfrac{1}{2}\)- \(\dfrac{1}{4}\)+\(\dfrac{1}{8}\)-\(\dfrac{1}{16}\)+\(\dfrac{1}{32}\)-\(\dfrac{1}{64}\)<\(\dfrac{1}{3}\)

Answer 1

Đặt A = \(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+\dfrac{1}{32}-\dfrac{1}{64}\)

2A = \(2\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+\dfrac{1}{32}-\dfrac{1}{64}\right)\)

2A = \(1-\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{8}+\dfrac{1}{16}-\dfrac{1}{32}\)

2A + A = \(\left(1-\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{8}+\dfrac{1}{16}-\dfrac{1}{32}\right)+\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+\dfrac{1}{32}-\dfrac{1}{64}\right)\)

3A = \(1-\dfrac{1}{64}\)

3A = \(\dfrac{63}{64}\) < 1

hay 3A < 1

=> A < \(\dfrac{1}{3}\)

Vậy .................. (tự kết luận)