Question

Chứng minh rằng: 1/2-1/4+1/8-1/16+1/32-1/64 <1/3

Answer 1

 Đặt A=1/2−1/4+1/8−1/16+1/32−1/64A

         =1/2−1/4+1/8−1/16+1/32−1/64
     2A=1−1/2+1/4−1/8+1/16−1/32

    2A =1−1/2+1/4−1/8+1/16−1/32
    3A=2A+A=1−1/64<1

   ⇒A<1/3

k cho minh nha

Answer 2

mình cũng khó câu này ai giúp mình với

Answer 3

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

\(\Rightarrow2A=1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}-\frac{1}{32}\)

\(\Rightarrow2A+A=\left(1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}-\frac{1}{32}\right)+\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}\right)\)

\(\Rightarrow3A=1-\frac{1}{64}< 1\)\(\Rightarrow A< \frac{1}{3}\left(đpcm\right)\)

                                  Vậy \(A< \frac{1}{3}.\)